
Class. 
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COEKIGUT DEPOSIT. 



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THE INTERRELATIONS OF MENTAL 
ABILITIES 



BY 

FREDERICK WILLIAM STEACY, Ph.D. 



TEACHERS COLLEGE, COLUMBIA UNIVERSITY 
CONTRIBUTIONS TO EDUCATION, NO. 95 



PUBLISHED BY 

(FrarlTpra (Enllrge, (Columbia Hnturnrita 

NEW YORK CITY 

1919 



.I* 1 



^51 



\ 

Copyright, 1919, by Frederick William Steacy 



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f £B -8 B22 



©SI.AS54578 



CONTENTS 

SEC. PAGE 

i The Tests and Their Administration i 

2 The Nature of the Abilities Measured: Interre- 

lations of the Several Tests 38 

3 The Composite Abilities and Their Interrela- 

tions 49 

4 The Hierarchy of the Specific Intelligences 52 

5 Sex Differences 58 

6 Individual and Composite Scores 62 

7 Bibliography 78 

8 Acknowledgments 79 



SECTION I 
THE TESTS AND THEIR ADMINISTRATION 

Thirty-two kinds of tests were used in this study, comprising 
those listed on page 2. In general, two tests of each kind were 
given, similar in form but varying in content. In some cases 
only one test was given, it being divided arbitrarily into two 
halves for scoring. Ai and A2 were such ex post facto halves. 
So also were A3 and A4, B3 and B4, D3 and D4. In two cases 
the scores from four (or five) tests were consolidated into two 
scores, making Ay and A8, and E9 and Eio. In five cases the 
same test was given the second time and both scores were used, 
making C3 and C4, C5 and C6, Cy and C8, En and E12, E13 
and E14. 

The subjects were the children of two classes, the 6B1 and the 
6B2 of the Bronx Public School No. 51. The two class rooms 
were adjacent. The two teachers who taught these two classes 
used the departmental method of instruction, i.e., they divided 
the subjects to be taught equally between themselves and each 
taught her allotted subjects to both classes, both classes receiving 
exactly the same instruction. The two classes contained, at the 
time the writer began to make his tests, 37 boys and 46 girls. 
For various reasons, to be explained later, the records of only 31 
boys and of only 38 girls were used in the composites and final 
calculations. The records of the two classes have not been kept 
separate, though the records of the two sexes have been carefully 
kept apart. Throughout the whole series of experiments the 
pupils showed marked interest and a strong desire to do good 
work. So far as pressure of work would permit, each day the 
writer read to the classes the results of the previous day's tests, 
that is, of the six or eight best in each class. As evidence of their 
interest it may be noted that the pupils showed admirable care 
of the mechanical tests, very few pieces being damaged or lost. 

The tests were given during the spring semester of 1916. Those 
of the Ventilation Commission were given during February, 
March, and April, while the other tests were given during May 
and June. The former were given with notable care by expert 
psychologists. The latter were given either by the writer or in 



2 The Interrelations of Mental Abilities 

THE ABILITIES MEASURED 

DIS- DIS- 
tinct tinct 
Manipulative Tests tests scores 

Al & A2 Stenquist Construction Test Single Series 1 1 2 

A3&A4 Stenquist Recognition of Mechanical Devices 1 2 

A5 & A6 Knot Making Test 2 2 

A7 & A8 Metal Puzzles 4 2 

A9&A10 Diagram Matching 2 2 

Al 1 & A12 Diagram Drawing 2 2 

A13&A14 Handwriting 2 2 

Non-verbal Spatial Relations Tests 

Bl Rogers' Superposition 1 1 

B2 Thurstone Spatial Relations 1 1 

B3&B4 Rogers' Locus or Space Intuition Test 1 2 

B5 Briggs' Similar Figures 1 1 

B6 Briggs' Congruent Figures 1 1 

Non-verbal Computational Tests 

CI & C2 Bonser's 2A and 2B 2 2 

C3&C4 Woody Addition 1 2 

C5&C6 Woody Subtraction 1 2 

C7&C8 Woody Division 1 2 

Arithmetic Tasks Stated in Words 

Dl & D2 Bonser's 1A and IB 2 2 

D3&D4 Starch's Arithmetic Scale 1 2 

D5&D6 Teachers College Arithmetic VI and VI(a) 2 2 

Very Verbal Tests 

El Briggs' Transitive Verbs 23 1 1 

E2 Briggs' Phrases 24 1 1 

E3 & E4 Starch's Grammatical Scales A and C 2 2 

E5 & E6 Van Wagenen's Mixed Relations 2 2 

E7 & E8 Woodworth and Well's Mixed Relations modified 

by Thorndike 2 2 

E9&E10 Thorndike's Reading Tests Alpha and I, J, K, L 5 2 

E11&E12 Thorndike's Directions V 1 2 

E13&E14 Thorndike's Visual Vocabulary Scale A 1 2 

E15&E16 Thorndike's Visual Vocabulary XII and VIII... 2 2 

El 7 Thorndike's Visual Vocabulary IX 1 1 

E18 Thorndike's Directions VII 1 1 

Logical Tests 

Fl & F2 Briggs' Faulty Arguments 37 and 39 2 2 

F3&F4 Briggs' Catches 41 and 42 2 2 

52 56 



The Tests and Their Administration 3 

his presence. All tests were given to the children in any one 
class under the same conditions, as a group test. It was fre- 
quently impossible to give to each class the same test on the 
same day, since, for example, the Knot test required some 8 to 
10 minutes for scoring each pupil. Six to eight hours' work on 
the test was therefore necessary before it was ready to be given 
the second time. The Construction test and each series of the 
Puzzle test likewise required several hours for scoring. The paper 
tests were given as far as possible to both classes on the same 
day. The administration began usually at 1 145 p.m. and closed 
about 2:50 p.m., that is, one-half hour for each class. Moreover, 
the order in which the classes were taken from day to day was 
alternately 6B1 and 6B2. The class-room teacher was usually 
present, but took no part in the administration of the tests. 

Group A. Construction or Mechanical or Motor Tests 

A 1 & A2 The Stenquist Construction Test Single Series 1 

The time for the whole test is 30 minutes. 

Source. This test has been devised by Mr. John Langdon Sten- 
quist, a graduate student of Teachers College, who, however, has 
not published any articles on this particular test, though he has 
published several articles on other and similar tests. 

Description. The material for this test is contained in a wooden 
box, 24 inches long, 5-5 inches wide and 2 inches high, fitted with 
hinges and containing eleven compartments, in each of which is 
a mechanical device, which is of full size and standard quality, but 
has been taken to pieces. The only tool needed is a screwdriver, 
and one of these is placed in each box. 

Presentation. To each pupil is given a slip of paper upon which 
to write his name. He is instructed to place this slip in the box. 
Then to each pupil a box is given, which is placed before the 
pupil with the hinges toward him. He is told that when he opens 
the box he may use the cover for a tray in which to keep the 
pieces, and he is advised to take the pieces out of one compart- 
ment and to complete the device and put it back before he disturbs 
another. This advice is given to prevent the pieces from becom- 
ing mixed. He is told to begin at his left hand, and to work 
in order toward his right hand, and that the device is to be put 
together so that it will work properly. Then the signal is given 



The Interrelations of Mental Abilities 



to begin. The usual signal in this and in all other tests in this 
series is : "Ready ! Hands up ! Go !" 

Method of Scoring. For each device which is properly put 
together so that it will work correctly 10 marks are given. For 
partial success partial credit is allowed according to the sub- 
joined scheme of marks. For the purpose of correcting for 
attenuation this test was scored in two parts. Ai represents 
the score for the alternate odd devices and A2 for the alternate 
even devices. The highest possible score is no marks for the 
whole test. 

Scheme for Scoring the Stenquist Construction Test Single Series 1 

A Bicycle 
Wrench 

B Ten Link 

Chain 
C Rubber Hose 

Clamp 

D Bicycle 
Bell 

£ Paper Clip 



F Metal 

Money Safe 

G Spring 
Clothespin 

H Gas 
Faucet 

/ Electric 

Push Button 
J Door 

Deadlock 

K Mouse Trap 



Head right = 2, nut right = 8, nut toward handle = 4, 
nut toward head = 2, head wrong and nut right =1, 
both wrong = 0. 

Each right link = 1, each half looped link= J4- 

Lever right = 10, lever reversed = 9, lever under- 
neath = 3. 

Lever right = 3, lever reversed = 1, spring right = 4, 
spring attached to wrong place = 2, cogwheel = 2, ham- 
mer = 1. 

Both levers right = 10, one lever right and one reversed 
= 9, both levers reversed = 8, levers wrong end in 
spring = 2. 

Center right = 2, center upside down = 1, the three 
springs = 1, each cap = 1, cover = 4. 

Both levers right =10, spring on tip of levers = 2. 

Tap right = 1, washer right = 2, washer reversed =1, 
holding screw = 1, regulating screw properly work- 
ing = 6. 

Peg = 1, spring = 1, base correctly fastened = 8. 

Lug = 1, bolt = 1, spring = 3, cover and screw = 1, 
key = 0, lug and bolt and spring = 0. 

Lever = 1, baitholder = 2, coil = 5, rivet = 0, complete 
trap = 10. 



A3 & A4 The Stenquist Recognition of Mechanical Devices 

Tests 

The time for this whole test is 30 minutes. 

Source. As the name implies, this test, like Ai & A2, has 
been devised by Mr. Stenquist. Nothing has hitherto been pub- 
lished concerning this test. 



The Tests and Their Administration 5 

Description. The test consists of a sheet of foolscap paper con- 
taining a space for the pupil's name, the date, etc., and a list 
of the names of fifty-five mechanical devices and also a stout 
cardboard box 18.25 inches long, 9.25 inches wide and 1.75 inches 
high. This box contains fifty-five mechanical devices correspond- 
ing to the names on the list. Each tool, which is of standard 
size and quality, is numbered and is fastened securely to the 
bottom of the box. 

Presentation. To each pupil is given a sheet of paper and a 
box. When each one has written his name, the purpose of the 
test is explained. The pupil is to find the mechanical device in 
the box which corresponds to its name on the list and then to 
write on the list and opposite the name the number of the device. 
At the usual signal the pupils begin work. 

Method of Scoring. For each device properly identified one 
mark is allowed. For the purpose of correcting for attenuation, 
this test was scored in two parts. A3 contains the devices num- 
bered 1 to 28, inclusive, and A4 contains the devices numbered 
2 9 t° 55, inclusive. The highest possible score for the whole 
test is 55 marks. 

A copy of the sheet used in this test is shown below : 

Department of Educational Psychology 
A3&A4 

RECOGNITION OF MECHANICAL DEVICES 

Test I Series I 

Name Age years months. 

Sex Grade School 

a. Bushing for packing nut of spark plug. 

b. Cabinet door hook. 

c. Carriage bolt. 

d. Catch for cabinet door hook. 

e. Central insulation for spark plug. 

/. Center punch. 

g. Common ten penny nail. 

h. Common wasber. 

i. Coping saw blade. 

;'. Cotter pin. 

k. Curtain rod fixture. 

/. Cut nail. 

m. Dowel screw. 

n. Drive hook. 

o. Drill. 

p. Eight penny finishing nail. 

q. Expansion lug nut. 

r. Flat head harness rivet. 



The Interrelations of Mental Abilities 

-s. Flat head wood screw. 

-t. Fuse wire. 

-u. Gasket or washer for making hose coupling tight. 

-v. Gimlet. 

-w. Glazier's point for fastening glass in window. 

-x. Hack saw blade. 

-z. Hinge. 

-al. Insulating plug for electric light wire in lamp. 

-61. Jam nut, or first nut for top of spark plug. 

-c\. Lock washer. 

-dl. Machine bolt. 

-el. Main body of spark plug. 

-/I. Nail set. 

-g\. Packing nut for spark plug. 

-hi. Patent box or mitre frame fastener. 

-tl. Picture nail. 

-/I. Pipe reducer bushing. 

-kl. Plumb bob. 

-II. Roller skate wrench and key. 

-ml. Round head rivet. 

-»1. Saw screw. 

-ol. Shade fixture for non-revolving end of shade roller. 

-pi. Shelf stop or support. 

-ql. Set screw. 

-rl. Small hasp. 

-si. Soft solder. 

-tl. Staple for small hasp. 

-wl. Stove bolt. 

-vl. Tar paper nail cap, to prevent nail head from tearing paper. 

-wl. Thumb nut. 

-xl. Trunk caster. 

-yl. Wedge to prevent window from rattling. 

-si. Wedge for tool handles. 

-a2. Window sash fastener. 

-b2. Window lift. 

-c2. Window shade fixture for revolving end of shade roller. 



A5 & A6 Knot Making Test. Ruger-Mandl Series I and Ruger- 
Mandl Series II 

The time for each series is 30 minutes. 

Source. This test has been designed by Professor Ruger. of 
Teachers College, and constructed by Mr. M. M. Mandl, a grad- 
uate student of the Department of Psychology in Columbia Uni- 
versity, though the writer contributed some thought and energy 
to the selection of the knots and to the preparation of the ma- 
terial. Nothing has hitherto been published on these series. 

Description. The material for this test is contained in a stout 
manilla envelope 12 inches long and 10 inches wide. Each enve- 
lope contains fifteen folders, each 11 inches long by 9 inches 
wide, numbered consecutively from 1 to 15, inclusive. Each 



The Tests and Their Administration 




KNOT MAKING TEST. SAMPLES OF KNOTS. 



8 The Interrelations of Mental Abilities 

folder contains upon its inside front cover a drawing of the 
knot to be made, and a loose piece of cardboard, 10.5 inches 
long by 7.25 inches wide, to which is attached, by two rubber 
bands, one piece of sash-cord if the knot to be made is single, 
and two pieces of sash-cord if the knot to be made is double. 
The knots to be made are arranged in the order of difficulty, as 
estimated from many preliminary trials. 

Presentation. The two series were given on different days. 
To each pupil was given a slip of paper upon which to write his 
name, etc., and he was asked to place this paper in his envelope. 
The envelopes were then distributed and placed so that the flap 
was uppermost and toward the pupil's right hand. He was in- 
structed upon opening the envelope to take out the top folder, 
to open it and to make with the piece of cord a knot like the 

Series A 5 









Pieces 


Length 


Name 


Number 


Marks 


of Cord 


of Cord, 
Inches 


Figure Eight 


1 


Oorl 




17 


Slip 


2 


Oorl 




19 


Hitch 


3 


Oorl 




24 


Reef 


4 


Oorl 




24 




5 


or 1 or 2 




25 


Double Bowline. . . . 


6 


0or2 




34 




7 


0or2 


2 


11 each 


Weaver's 


8 


0or2 
0or2 




34 




9 


30 




10 


0or2 




24 




11 


0or3 




30 




12 


or 1 or 2 or 3 




30 




13 


or 1 or 2 or 3 


or 4 1 


30 




14 


or 1 or 4 




34 




15 


Oor 2 or 5 




34 


Series A 6 










Reef 


1 


Oorl 


2 


10 each 


Hitch 


2 


Oorl 




20 




3 


Oorl 
Oorl 


2 


10 each 




4 


20 


Hitch 


5 


or 1 or 2 




19 




6 


Oor 1 or 2 




19 




7 


Oor 2 


2 


11 each 




8 


Oor 2 




23 




9 


Oor 3 
Oor 2 




19 




10 


24 




11 


Oor 2 




19 




12 


or 1 or 3 




30 




13 


Oor 2 or 4 




28 




14 


Oor 1 or 2 or 3 


or 4 1 


34 




15 


or 3 or 5 




35 



The Tests and Their Administration 9 

diagram and to place the knot upon the cardboard, fastening 
it there by the rubber bands; then to put the cardboard back 
into its folder and to put the folder back into the envelope under- 
neath the others, and then to take another folder, etc. 

Method of Scoring. Since the knots differ in difficulty the 
marks vary according to the subjoined scheme, the highest pos- 
sible score being 35 marks for each series. (See page 8.) 

A7 & AS Ruger Puzzle Series I, II, III, IV 
Series I. 

The time for this series is 15 minutes. 

Source. Puzzles Nos. 1, 2, 3, 4, and 5 were designed by Pro- 
fessor Ruger, of Teachers College, and were shaped and brazed 
by the writer in the workshops of Teachers College. Puzzle 
No. 6 was purchased ready made. Puzzles Nos. 7 and 8 were 
purchased and then modified by the writer. 

Description. Each puzzle consists of two parts. One part of 
puzzle No. 1 is made of No. 7 wire and the other part is made 
of No. 10 wire. Puzzles Nos. 2, 3, 4, and 5 are made of No. 10 
wire. Puzzle No. 6 consists of a finer wire. Puzzle No. 7 consists 
of a piece of sheet metal shaped like the conventional heart and 
pierced by six holes through each of which a cord is passed, and 
then looped and pulled taut. Puzzle No. 8 consists of a metal 
rectangle pierced by three holes through which a cord is passed 
and then looped and drawn taut. The ends of each cord are tied 
by a knot and the knot is secured by sealing wax. These eight 
puzzles are constructed largely on one principle. The eight are 
contained in a stout cardboard box 13.5 inches long, 6 inches 
wide and 1.25 inches high. The box has seven compartments, 
each containing one puzzle, except the seventh compartment, 
which contains two puzzles, i.e., puzzles Nos. 7 and 8. The 
compartments are numbered and the puzzles are arranged therein 
according to estimated difficulty. 

Presentation. A slip of paper for the name, etc., and a box 
of puzzles were given to each pupil with instructions to separate 
each into two parts, without the use of force. 

Method of Scoring. One mark was allowed for each puzzle 
which was separated into two parts without damage to the puz- 
zle. The highest possible score is eight marks. 



io The Interrelations of Mental Abilities 

Series II. 

The time for this series is 15 minutes. 

Source. The metal parts of these puzzles were designed by 
Professor Ruger and shaped by the writer. The leather parts 
were made by a neighboring shoemaker. 

Description. This series consists of three puzzles. The prin- 
ciple of the three is identical, but the second is much more diffi- 
cult than the first, while the third is very much more difficult 
than the second. Each consists of two parts. One part is a 
leather band about one- fourth inch wide. The other part is 
made of No. 10 wire. The three puzzles are contained in a 
stout cardboard box 7 inches long, 5.5 inches wide and 1 inch 
high. Each box has three compartments, one for each puzzle. 

Presentation. A slip of paper for the name, etc., and a box of 
puzzles were given to each pupil, with instructions to remove 
the leather strap from the metal part without the use of force. 

Method of Scoring. Four movements are necessary for the 
solution of puzzle No. 1, nine movements for puzzle No. 2 and 
nineteen movements for puzzle No. 3. For each movement 
properly made one mark is allowed. Each pupil, however, re- 
turned the puzzles usually wholly apart or wholly together, there- 
fore very few marks were given for partial solutions. The 
highest possible score is 32 marks. 

Series III. 

The time for this series is 30 minutes. 

Source. These puzzles (Chinese rings) were purchased ready 
made, but were later modified by the writer. 

Description. This series consists of five puzzles, all identical 
except in the number of the rings. Puzzle No. 1 has two rings, 
puzzle No. 2 has three rings, puzzle No. 3 has four rings, puzzles 
Nos. 4 and 5 have five rings each. In order to prevent the slip- 
ping of the frame carrying the rings, from the bar to the handle, 
and thus delaying and probably perplexing the pupil, a piece of 
strong string was tied around the narrow part, between the bar 
and the handle, and this string was protected by a thick covering 
of sealing wax. These five puzzles are contained in a box, similar 
in all respects to the box of series No. 1, except that the boxes 
for series No. 3 contain five compartments, which are numbered 



The Tests and Their Administration u 

from i to 5. The puzzles are arranged therein according to 
their difficulty. In order to prevent the rings from slipping 
wholly off the bar a paper clip, the same as in Test Ai & A2, 
was placed over the point of the bar. 

Presentation. To each pupil were given a slip of paper for the 
name, etc., and a box of puzzles, with instructions to remove 
first the clip and then to separate, without damaging the puzzles, 
the frame carrying the rings from the bar, and then to place the 
clip back on the point of the bar. The purpose of the clip was 
carefully explained to the pupils. 

Method of Scoring. For the solution of the two-ring puzzle, 
two movements are necessary ; for the three-ring puzzle, five 
movements ; for the four-ring puzzle, ten movements ; and for 
the five-ring puzzle, twenty-one movements. For each movement 
properly made one mark is allowed. The highest possible score 
is 59 marks. 

Series IV. 

The time for this series is 30 minutes. 

Source. These puzzles and their boxes were purchased ready 
made. Several of the puzzles were separated by the writer into 
their component parts and recombined. 

Description. This series consists of fifteen puzzles. No two 
are alike, though three form one group differing only in the 
number and the arrangement of the parts, while four others form 
another group likewise differing only in the number or the 
arrangement of the parts. The boxes are 12.5 inches long, 7.75 
inches wide and 1 inch high. Each box has fifteen compart- 
ments, that is, one compartment for each puzzle. All these 
puzzles are made of stout steel wire, nickel plated, except one 
which is made of cast iron. 

Presentation. A slip of paper for the name, etc., and a box 
were given to each pupil, with instructions to separate the puzzles 
into their parts. The pupils were told that they might use force 
in separating any, except the puzzle which was made of cast 
iron. They were told that they might begin the puzzles in any 
order but were advised that the puzzles at their left hand were 
on the whole easier than those on their rijrht hand. 



12 



The Interrelations of Mental Abilities 



Method of Scoring. The marks allowed varied partly accord- 
ing to the estimated difficulty and partly according to the number 
of easily distinguishable movements necessary for the complete 
solution. Two puzzles were allowed one mark each ; two puzzles 
were allowed two marks each; five puzzles were allowed three 
marks each; four puzzles were allowed four marks each; one 
puzzle was allowed five marks; and one puzzle was allowed six 
marks. The highest possible score is forty-eight marks. Partial 
credit was allowed according to the number of correct moves 
which had been made. 

Test Ay consists of Series I and Series IV. 

Test A8 consists of Series II and Series III. 

Ao & 10 Diagram Matching Test, Two Series: A and B 

The time for each of these two series is 14 minutes. 

Source. The writer received the idea for this test and for 
the next succeeding test from the Binet-Simon series. The pro- 
totype is given by de Fursac (191 3; pp. 437-38), as test No. 54. 
He calls it a test for imagery of form and assigns it to children 





/L_ N ^t^x 



N — V X_7 




SECTION OF DIAGRAM MATCHING TEST. 



The Tests and Their Administration 



13 



of thirteen years. The prototype is given also by Goddard (1911, 
p. 9) in his revision under the title "Cutting Out," and he assigns 
it to adults. The writer's purpose was to obtain a non-verbal 
test for imagery of form, which (1) would be much easier than 
the Binet-Simon tests and which (2) could be given to a large 
group at one time, and which (3) could be easily scored. The 
test as modified seems to fulfill all these conditions. 

Description. The two series of this test are similar and have 
been evolved on the same principle. They are of equal or of 
nearly equal difficulty, since the 100 diagrams which compose 
tests A9, Aio, An, A12 were drawn at one time in such a way 
that the 100 diagrams are really twenty-five groups of four each, 
these four being identical with each other except in orientation. 
For the Matching tests twenty groups were selected and from 
each group one was taken for series A9 and another was taken 
for series Aio. The test consists of two sheets of paper. One 
sheet contains twenty diagrams, which are symmetrical, so far as 
their quarters are concerned. This sheet contains blank spaces 
for the name, etc. The other sheet contains the Upper Left Hand 
Quarters of the diagrams of the first sheet, but the order of the 
figures in the two sheets is quite different. The Upper Left Hand 
Quarters are numbered consecutively. 

Presentation. Two diagrams, which are not in these series, 
were drawn on the blackboard, and also their Upper Left Hand 
Quarters. The tests were explained and described from the 
blackboard. The pupils were told that they would be required 



r 



1_ 



f 



^s 



IZ 



13 



u\ 



'7 \y %> \!/ r 

DIAGRAM MATCHING TEST. UPPER LEFT HAND CORNERS. 




14 The Interrelations of Mental Abilities 

to compare the figures on the two sheets and to select the whole 
diagram corresponding to the Upper Left Hand Quarter and to 
write in the whole diagram the corresponding number. These 
tests, like all the other paper tests, are given face down and at the 
usual signal are upturned and immediately the time is taken and 
the task of solution is begun. The two series were given on differ- 
ent days. 

Method of Scoring. One mark was allowed for each diagram 
properly identified. No penalty was imposed for errors. In scor- 
ing, a shield was used having an opening corresponding to each 
whole diagram and properly numbered. This sheet, when laid on 
the sheet marked by the pupil, greatly facilitated the task of scor- 
ing and much diminished the chance of error. The highest possible 
score is 20 marks for each series. 

An & 12 Diagram Drawing Test, Two Series: C and D 

The time for each of these series is 30 minutes. 

Source. See above for A9 & Aio. 

Description. The two series of this test are similar and have 
been evolved on the same principle. They are of equal or of 
nearly equal difficulty, since the sixty diagrams which remained 
when the forty diagrams of A9 & A 10 were removed were 
equally divided. Two sheets were used for each pupil. The first 
sheet contains thirty figures.^ Each of these is the upper left 
hand quarter of the diagram to be drawn and bears its dis- 
tinctive number. The second sheet has forty dotted outlines all 
alike. The purpose of these outlines is to form a background 
on which the pupils can draw the required diagram, thereby 
greatly simplifying the task for him and also much facilitating 



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SECTION OF DIAGRAM DRAWING TEST. 



The Tests and Their Administration 15 

the labour of scoring. The diagrams are 1.5 inches long and 
the same in width. Each dotted outline has five equidistant lines 
parallel to the lower margin of the sheet, and five equidistant 
lines crossing these at right angles. 

Presentation. The purpose of the test was explained to the 
pupils at the blackboard, upon which were drawn some diagrams 
from the previously described test. Some dotted outlines were 
drawn and then filled in from the patterns. The pupils were 
told that the extra outlines were for use in case they spoiled 
an outline and that they were not required to draw the diagrams 
according to the order of the patterns, but to be careful to write 
in their drawing the number of the pattern. The use of rulers 
was allowed but was not encouraged. 

Method of Scoring. One mark was allowed for each diagram 
properly drawn. Neatness and beauty were not counted, since 
these tests are not of artistic ability, but of power to utilize 
ideas of form. To be correct, each angle must coincide with an 
intersection of the dotted lines in the background. Therefore 
subjective criteria for the appraisal of the drawing were wholly 
unnecessary. Two or three pupils left one diagram each incom- 
plete. If this were correct partial credit might be given for it 
by a finer system of scoring, but the cases were so few as to 
cause but slight difference in the results. The highest possible 
score is 30 marks for each series. 

A13 & 14 Handwriting 

The material for this test was the papers belonging to the 
other tests. Two of the written tests were used for A13 and two 
other written tests were used for A 14. These samples were 
graded by two persons. The Thorndike Handwriting Scale was 
employed as the standard. The highest mark on this scale is 
eighteen. The papers were graded by quarter marks. In order 
to avoid fractions these quarter marks were multiplied by four. 
Since the scores of the two judges were combined the highest 
mark possible for test A13 or A14 was 18x2x4x2 = 288. The 
highest mark actually given to any sample was 16. The pupils 
were advised to write legibly but on the whole very little emphasis 
was laid upon the handwriting portion of the series. The object 



16 The Interrelations of Mental Abilities 

was to obtain, not the best copy-book style, but the best ordinary 
samples. 

Group B. Non-Verbal Spatial Relations Tests 
Bi Superposition Test 

The time for this test was 2 minutes. 

Source. This is a modification, for the sake of simplification, 
by Miss Rogers. 1 of Thurstone's Spatial Relations Test, which 
will be described in test B2. 

Description. This test requires the recognition of plane geo- 
metrical figures, all being equal and symmetrical rhombuses, each 
side being one-half inch in length. Each rhombus has for one 
side a heavy line, which may make any angle with the margin 
of the paper, provided only that one side of the rhombus be 
parallel to some one margin of the paper. Twenty-four such 
rhombuses are arranged in two columns. Each contains a small 
circle in one corner, in any corner so far as the heavy line and 
the margin of the paper are concerned. Opposite to each of 
these rhombuses are two rhombuses without circles. These have 
the heavy line parallel with the base margin and toward it. 
Moreover, this heavy line is continuous between the two and 
projects about an eighth of an inch beyond each. The two upper 
corners of the two rhombuses are one-fourth of an inch apart, 
while the two lower corners are three-fourths of an inch apart. 

Presentation. This test was given by Miss Rogers in the 
writer's presence. Explanations were given at the blackboard, 
and some practice was allowed before the material for the actual 
test was distributed. The pupils were required to find the one 
of the two rhombuses which corresponded to the rhombus with 
the circle and then to draw the circle in the corresponding 
corner. 

Method of Scoring. One mark was allowed if the circle was 
placed in the proper diagram, and two marks were given if the 
circle was drawn not only in the proper diagram, but also in 
the proper corner. Nothing was allowed if the wrong diagram 
was marked. The highest possible score was 48 marks. 

1 Rogers, A. L., Tests of Mathematical Ability and Their Prognostic 
Value, Teachers College. 



The Tests and Their Administration 17 

B2 Thurstone Spatial Relations Test 

The time for this test is 2.5 minutes. 

Source. This test was devised by Dr. L. L. Thurstone, of the 
Pittsburgh Institute of Technology. 

Description. The test is the same in all respects as the Super- 
position test described above, except that before identifying the 
rhombus it must be imaginatively turned face downwards and 
back upwards. 

Presentation. This test was given by Miss Rogers in the 
writer's presence. The test was explained at the blackboard 
and some time (1 or 2 minutes) was permitted for practice 
before the test sheets were distributed. 

Method of Scoring. The same as in Bi. 

Instructions. Prepare three cardboards similar to the three 
cards shown on the instructions side of the sheet. Make these 
cards about 10 inches on the side. Paint one edge of each card 
black on both sides of the card. Cut the holes as indicated. 

Before giving the test, draw on the blackboard the complete 
drawing on the instructions side of the blank. This need not 
be done very accurately. 

Spatial Relations Test 

Assume that the lozenge shaped figure with a circle in it represents 
a small card with one of its edges painted black and with a hole in one 
corner. 

Imagine that this card is picked up, turned over, and placed face 
down with the black edge of the card touching the long heavy black line 
to the right. Imagine the card moved along this black line until its edges 
fit the edges of one or the other of the lozenge shaped outlines. 

With your pencil draw a circle in the comer where the hole will be. 

Proceed in the same manner and as rapidly as you can with the 
remaining outlines on the page. 

Page I 



w n va 




i8 



The Interrelations of Mental Abilities 



Page 2 




Allow two minutes for the group to read the instructions, 
warning them that the instructions must be read carefully to 
be understood. 

At the end of this time limit, repeat orally the marked portion 
of the instructions ("Imagine" . . . "hole will be") while 



The Tests and Their Administration 19 

moving one of the large cardboards into place on the blackboard 
drawing. Give this paragraph verbatim for each of the three 
cards, on the instruction side. 

Then give the test proper with a time limit of two minutes. 
I have found three subjects who finished the blank with 24 
correct responses in less than the time allowed, but the majority 
of students make hard work of it and require considerably more 
than two or three minutes per column. If the test can be given 
as an individual test, it would be advisable to take the time for 
each column and thus obtain a reliability measure for the test. 
This is hardly practicable when giving it as a group test on 
account of the great range of speed. 

B3 & B4 Locus Test or Space Intuition Test 

The time for this test was not limited. Each pupil was per- 
mitted to work as long as he wished. The maximum time was 
15 minutes. 

Source. This test was prepared by Miss Rogers. Nothing 
has hitherto been published on this test. 

Description. The paper, as given to the pupils, has two 
examples properly answered for the purpose of illustration and 
nine questions for the test. As the name implies the test is 
geometrical but unconventional. 

Presentation. The test was given by Miss Rogers in the 
writer's presence. 

Method of Scoring. For a perfect answer two marks are 
given and for an answer half right one mark is given. The 
highest possible score is 18 marks. For the purpose of correct- 
ing for attenuation the test was divided into two parts, though 
given as a whole. B3 consists of the alternate odd questions and 
B4 of the alternate even questions. 

There is much doubt concerning the propriety of including 
this test in the non-verbal group, considering the age and train- 
ing of the pupils tested. On the other hand, it is equally or 
more unsatisfactory to treat it as a verbal test. Its complex 
nature should be kept in mind when its correlations are dis- 
cussed. 



20 



The Interrelations of Mental Abilities 



Name 



Space Intuition Test (1) 
Date. 



Example a) If a pencil moves on this paper 1 inch 
from the right-hand edge, draw the path 
followed by the point of the pencil. 

b) Show by a drawing the kind of line that 
passes through all the houses one mile 
from a certain point. Let — =1 mile. 



2. Show by a drawing in the space opposite, the path 
of a point that is always half-way between the 
tip of the hour-hand of a watch and the rim. 



3. A number of equal circles are drawn between two 
parallel straight lines and touching them both. 
Show by a drawing in the space opposite where 
their centres must be. 



A pencil is attached to a string. The string and 
pencil are held as if a circle were to be drawn, 
but while the pencil moves round the fixed point 
at which the string is held, the string is gradually 
lengthened. Draw in the space opposite, the path 
marked by the pencil point. 



1. A motor boat sails up a straight canal midway 1. 
between the banks. Draw in the space opposite 
the path of the boat. 



4. 



5. Draw in the space opposite, the path followed by 
the tips of a pair of shears, when the bolt or screw ' 
remains always fixed in one position. The scissors 

do not move forward or back. They simply open 

and shut. 6. 



A boy starts from the southwest corner of a square 
and walks in a northeasterly direction. Draw in 
the space opposite, the path he follows. 

a) If for every foot he walks East, he walks 1 

North. 

b) If for every foot he walks East, he walks 2 

North. 

c) If for every foot he walks East, he walks ^ 

North. 



7. Show by a drawing in the space opposite, how a 
road would have to be constructed so as to be 
everywhere the same distance from two houses, 
A and B. 7. 




B 



The Tests and Their Administration 21 

B5 Similar Figures 

The time for this test is 3 minutes. 

Source. This test is No. 17 of Briggs' tests published in 1913. 1 

Description. The test consists of four odd figures and eight 
pairs of figures. The members of a pair are alike in all respects 
except in size or orientation. The twenty figures are arranged 
in five columns of four figures each. The members of a pair 
are never adjacent in a column or in a row. 

Presentation. At the head of the sheet instructions are given : 
"Figures are similar when they are exactly alike in shape. Find 
pairs of similar figures and write in parentheses the numbers 
representing each pair, e. g., (21, 53)." Before the papers were 
distributed some oral instructions were given. 

Method of Scoring. In order to avoid negative scores, 8 marks 

were added to each score. The highest possible score is 16 

marks. 

For each pair correctly marked = 1 

For error in the star figures = — 1 

For each other error = — 2 

For unattempted or meaningless = — 8 

B6 Congruent Figures 

The time for this test is 3 minutes. 

Source. This test is No. 18 of Briggs' test. 2 

Description. This test consists of four odd figures and eight 
pairs of figures. The members of a pair are alike in all respects 
except in orientation. The twenty figures are arranged in five 
columns of four figures each. The members of a pair are never 
adjacent either in a column or in a row. 

Presentation. At the head of the sheet instructions are given : 
"Figures are congruent when they are exactly alike in shape 
and size. Find pairs of congruent figures and write in paren- 
theses the numbers representing each pair, e. g., (21, 53)." Be- 
fore the papers were distributed some oral instruction was 
given. 

Method of Scoring. The same as for B5. 

x Teachers College Record, September, 1913, p. 25. 
'Ibid., p. 26. 



22 The Interrelations of Mental Abilities 

Group C. Non-Verbal Computational Tests 
Ci 

The time for this test was 6 minutes. 

Source. This test is No. nA as printed in Bonser (1910, 
p. 2) 1 and No. 35 in Briggs (1913, p. 34). 2 

Description. Dr. Bonser described this test as composed of 
one-step problems stated in a manner less conventional than 
usual, and regards them as a test of reasoning activity and of 
mathematical judgment. The test consists of five problems. 
Owing to a typographical error in Dr. Bonser's thesis this test is 
different from the form in which he gave it though agreeing 
with the book. The test here agrees with his book which reads 
"132 plus what number equals 36?" While his test as used by 
him read "32 plus what number equals 36?" 

Presentation. This test was conducted in the same way as 
all other paper tests, except that the pupils were told that this 
test would be in arithmetic. 

Method of Scoring. One mark was given for each correct 
answer. The highest possible score is 5 marks. 

C2 

The time for this test was 3 minutes. 

Source. This test is No. 11B in Bonser (1910, p. 2) and No. 36 
in Briggs (1913, p. 34). 

Description. This test parallels Ci above. 

Presentation. The same as in Ci above. 

Method of Scoring. The same as in Ci above. The highest 
possible score is 5 marks. 

C3 & C4 Addition 
The time for this test was 25 minutes. 

Source. This is a preliminary series prepared and used by 
Woody in the preparation of his Addition Scale (1916). 3 

'Bonser, F. G., Reasoning Ability of Children in Grades 4, 5, 6, 
Teachers College, 1910. 

'Teachers College Record, September, 1913. 

"Woody, C, Measurements of Achievement in Arithmetic, Teachers 
College. 1916. 



The Tests and Their Administration 23 

Description. The test has 38 questions. It embraces the 
addition of one-place, two-place, three-place, and four-place 
integers, of decimal currency, of proper fractions, of mixed 
fractions, of decimals, and of compound numbers. 

Presentation. This test was given twice, once in February 
and once in April. 

Method of Scoring. One mark was given for each question 
which was answered correctly. The highest possible score was 
38 marks. 

C5 & C6 Subtraction 

The time for this test was 20 minutes. 

Source. The same as C3 & C4, in subtraction. 

Description. This test has 35 questions. It embraces the 
subtraction of simple integers, of proper fractions, of mixed 
fractions, of decimals, and of compound numbers. 

Presentation. The same as in C3 & C4 above. 

Method of Scoring. The same as C3 & C4 above. The highest 
possible score was 35 marks. 

Cy & C8 Division 

The time for this test was 30 minutes. 

Source. The same as C3 & C4, in division. 

Description. This test has 36 questions. It embraces the 
division of simple integers, of decimals, of vulgar fractions, of 
mixed fractions, and of compound numbers. 

Presentation. The same as in C3 & C4 above. 

Method of Scoring. The same as in C3 & C4 above. The high- 
est possible score was 36 marks. 

These three tests are similar to but not identical with Series 
A, Woody (1916). 

Group D. Arithmetic stated in Words 

Di & D2 Problems 

The time for these two series is 3 minutes each. 
Source. These are iA and iB in Bonser (1910, p. 2) and 
No. 33 and No. 34 in Briggs (1913, p. 33). 
Description. Each test consists of five two-step problems. 
Presentation. The same as in Ci. 



24 The Interrelations of Mental Abilities 

Method of Scoring. The same as in Ci. The highest possible 
score is five marks for each series. 

Z)? & D4 Arithmetic Scale 

The time for this whole test is 20 minutes. 

Source. This test is by Dr. Daniel Starch (1916, p. 213). l 

Description. This test consists of a graded series of problems 
of the sort ordinarily found in text-books. 

Presentation. The same as in Ci. 

Method of Scoring. One mark was allowed for each correct 
answer. The twelve questions were given on one sheet and 
afterwards divided for the purpose of correcting for attenuation. 
D3 consists of the alternate odd questions and D4 of the alter- 
nate even questions. The highest possible score for the whole 
paper is 12 marks. 

D5 & D6 Problems. Two Series: Tests VI and VI (a). 

The time for these series was 30 minutes each. 

Source. The Laboratory of Educational Psychology, Teach- 
ers College. 

Description. Each series consists of six problems, which 
become progressively more difficult. 

Presentation. The same as in Ci. 

Method of Scoring. One mark was allowed for each problem 
correctly answered. The highest possible score is 6 marks for 
each series. 

Test VI 

Write your name here 

Write the date here 

Find the answers to these problems. Do all your work on the sheets of 
white paper. Write your answers here. 

The answer to 1 is 

The answer to 2 is 

The answer to 3 is 

The answer to 4 is 

The answer to 5 is 

The answer to 6 is 

iStarch, D., Educational Measurements, 1916. 



The Tests and Their Administration 25 

Write your name on every sheet of white paper that you use and hand in 
all the sheets of white paper. 

1. There are 550 pupils on the roll. If $•£ of them are here to-day, 
how many are absent? 

2. A boy had 210 marbles. He lost 1/3 of them. How many were 
left? 

3. The children of a school made small boxes to be filled with candy 
and given as presents at a school party. 600 were needed. In 4 days 
grades 3 to 7 made 20, 25, 83, 150 and 150 boxes. The eighth grade agreed 
to make the rest. How many did the eighth grade make? 

4. A boy lost one-fourth of his kite string in a tree, one-third in some 
wire, and one-fifth in a hedge. What part of his string was left? 

5. How much will 8% dozen pencils cost at the rate of $J4 for a 
half dozen? 

6. John had $1.20 Monday. He earned 30 cents each day on Tuesday, 
Wednesday, Thursday and Friday. Saturday morning he spent one-third 
of what he had earned in four days. Saturday afternoon his father 
gave John half as much as John then had. How much did his father 
give John? 

Test VI (a) 

Write your name here 

Write the date here 

Find the answers to these problems. Do all your work on the sheets of 
white paper. Write your answers here. 

The answer to 1 is 

The answer to 2 is 

The answer to 3 is 

The answer to 4 is 

The answer to 5 is 

The answer to 6 is 

Write your name on every sheet of white paper that you use and hand in 
all the sheets of white paper. 

1. If $1991 a day is paid to 724 men who each earn the same wages, 
how much does each man receive? 

2. A baseball team played 160 games during the season and won 100 
of them. What part of the whole number of games did the team win? 

3. A store-keeper sold 12 yards of cloth, which was 4/15 of the whole 
piece. How many yards were there in the whole piece? 

4. A grocer had a tank holding 44 3/16 gallons of oil. One day he 
drew out 15}4 gallons and the next day 9y& gallons. How many gallons 
were left in the tank? 

5. One summer a farmer hired 43 boys to work in an apple orchard. 
There were 35 trees loaded with fruit, and in 57 minutes each boy had 
picked 49 apples. If in the beginning the total number of apples on the 
trees was 19,677, how many were there still to be picked? 

6. A boy had 3 dollars. He paid it all for four articles, which we will 
call A, B, C. and D. B cost as much as C. C cost as much as D. A cost 
as much as B, C and D together. The boy sold A and B for \y 2 times 
what he paid for them. He sold C and D for V/± times what he paid for 
them. How much did he get for the four articles? 



26 The Interrelations of Mental Abilities 

Group E. Very Verbal Tests 
Ei. Understanding and Applying a Definition: Transitive Verbs 

The time for this test was I minute, 30 seconds. 

Source. This test is No. 23 in Briggs (1913, p. 28). 

Description. This test consists of twelve simple sentences. 
Nine of them have a transitive verb in the active voice. One 
each of the other verbs is intransitive or copulative or passive. 

Presentation. Since the pupils had not received any school 
training in transitive verbs, the writer fearing that they would 
be confused by the printed instructions modified them to read 
"Mark the sentences with objects," i. e., 1, 2, 3, 7, 8, 9, 10, 11, 
12. The papers were thus scored and the results used herein. 
Since this modification may have increased the confusion the 
papers were scored also by the original method, i.e., 1, 2, 7, 11, 
and the correlations with E2 were computed. These are: boys 
-(-25 and girls — 01. The original method gives a slightly 
higher correlation than the modified method, though the average 
marks received by the pupils are much lower : boys 6.28 and 
girls 6.90. 

Method of Scoring. One mark was allowed for each sentence 
containing a transitive verb in the active voice which was checked 
and one mark for any other sentence which was not checked. 
The highest possible score is 12 marks. 

E2 Understanding and Applying a Definition: Phrases 

The time for this test was 2 minutes. 

Source. This test is No. 24 in Briggs (1913, p. 29). 

Description. The test consists of twelve sentences. Four of 
these sentences contain a phrase according to the instructions 
given as stated below. 

Presentation. At the top of each sheet two paragraphs are 
printed: "A phrase is a group of words not containing a subject 
and predicate and used like an adjective or an adverb. 

"Make a ^ by each sentence which, according to this definition, 
contains between the parentheses a phrase and nothing beside 
the phrase and its modifiers." 



The Tests and Their Administration 27 

Method of Scoring. One mark was allowed for each sentence 
which was checked correctly and one mark for each other which 
was left unchecked. The highest possible score is 12 marks. 

£3 & E4 Grammatical Scales: A and C 
The time for A was 12 minutes and for C 6 minutes. 
Source. These tests are by Starch (191 5, p. 615 and p. 620 ). 1 
Description. Scale A contains 37 sentences and Scale C 20 
sentences of various degrees of difficulty. Each sentence con- 
tains two or more words in parentheses between which choice is 
to be made. One of these alternatives is right and the other 
is wrong. 

Presentation. At the top of the paper for each scale direc- 
tions are printed as follows: "Each of the following sentences 
gives in parentheses two ways in which it may be stated. Cross 
out the one which you think is incorrect or bad. If you think 
both are incorrect cross both out. If you think both are correct 
underline both." These instructions were explained before the 
papers were distributed. 

Method of Scoring. One mark was allowed for each sentence 
which was properly lined. The highest possible score for scale 
A is 37 marks and for scale C is 20 marks. The key supplied 
by Dr. Starch was invariably followed, though, in the writer's 
opinion, some of the usages thus scored wrong are allowable. 

£5 & E6 Mixed Relations. Two Series 

The times was about 1 minute, 15 seconds for each half of each 
series. 

Source. The two series are developments of the Woodworth- 
Wells test, made by Mr. M. J. Van Wagenen, of the University 
of Minnesota. Nothing has hitherto been published upon these 
two series. 

Description. Three words are read and the pupils are re- 
quired to write the fourth word which must bear the same 
relation to the third word which the second bears to the first 
word. Each series consists of fifty such groups. 

journal of Educational Psychology, December, 1915. 



28 



The Interrelations of Mental Abilities 



Van Wagenen Mixed Relations Test — C 

Directions — Give at the rate of 5 seconds each— }4 second between 
each word and 4 seconds for the written response. 

1 Light 

2 Birds 

3 Chalk 

4 Sun 

5 Summer 

6 Cats 

7 Emerald 

8 Water 

9 Father 

10 Hat 

11 Chair 

12 Fast 

13 Cup 

14 Man 

15 Write 

16 Lamp 

17 Daily 

18 Hair 

19 Food 

20 Clothes 

21 Air 

22 Barn 

23 Month 

24 Far 

25 July 

26 Opaque 

27 Thermometer 

28 Potato 

29 Light 

30 Sight 

31 City 

32 Slipper 

33 Present 

34 Work 

35 Water 

36 Factory 

37 Fat 

38 Bread 

39 Live 

40 After 

41 Sparrow 

42 Picture 

43 Happy 

44 Ounce 

45 Mail 

46 Complex 

47 Linen 

48 Victory 

49 Cheap 

50 Pencil 

Presentation. These tests were given by Mr. Van Wagenen 

in the writer's presence. In addition to the directions printed 

at the top of the sheet, some oral explanations were given ; these, 



day 


Dark 


fly 


Fish 


white 


Carbon 


shines 


Wind 


hot 


Winter 


scratch 


Bees 


green 


Ruby 


drink 


Air 


son 


Mother 


head 


Shoe 


wood 


Stove 


fastest 


Great 


saucer 


Knife 


husband 


Woman 


stories 


Draw 


oil 


Stove 


newspaper 


Monthly 


black 


Eyes 


eat 


Books 


tear 


Dishes 


birds 


Water 


hay 


Library 


week 


Day 


near 


There 


month 


Friday 


wood 


Transparent 


temperature 


Clock 


vegetable 


Veal 


dark 


Dry 


blind 


Hearing 


mayor 


State 


shoe 


Cap 


known 


Future 


problems 


Play 


glass 


Coffee 


workman 


Store 


heavy 


Thin 


flour 


Candy 


die 


Life 


before 


Earlier 


bird 


Mosquito 


frame 


Field 


laugh 


Sad 


pound 


Inch 


write 


Telephone 


difficult 


Simple 


cool 


Wool 


defeat 


Success 


many 


Costly 


write 


Broom 






The Tests and Their Administration 



29 



however, were few since the pupils had had some experience 
with similar tests. A few minutes rest was allowed between each 
half. At the end of each half, another triad (25a and 50a) was 
given, being any one of the preceding except the next preceding, 



Van Wagenen Mixed Relations Test — D 



1 Work 

2 Vinegar 
Rain 
Year 
Iron 
Rose 
Country 

8 Eat 

9 Horn 

10 High 

11 Water 

12 Stove 

13 Snow 

14 Rugs 

15 Boston 

16 Silver 

17 Hard 

18 Triangle 

19 Delicious 

20 Number 

21 See 

22 Box 

23 Fruit 

24 Front 

25 Foot 

26 Raise 

27 Much 

28 Foot 

29 Sugar 

30 Navy 

31 River 

32 Coal 

33 Hair 

34 Grain 

35 Leg 

36 Park 

37 Baker 

38 Wall 

39 People 

40 Sit 

41 Bright 

42 Park 

43 Man 

44 Lilac 

45 Violet 

46 Under 

47 Kettle 

48 Fire 

49 Fork 

50 April 



day 

sour 

summer 

month 

heavy 

bush 

road 

food 

blow 

low 

liquid 

heat 

sledge 

floor 

city 

tarnishes 

soft 

three 

taste 

figures 

colors 

wood 

basket 

back 

ankle 

lower 

more 

leg 

bowl 

sailors 

Hudson 

black 

goat 

wheat 

knee 

play 

bread 

paper 

house 

sat 

colors 

gate 

legs 

shrub 

odor 

over 

utensil 

warms 

tine 

March 



Sleep 

Sugar 

Snow 

Week 

Aluminum 

Oak 

City 

Wear 

Bell 

Near 

Ice 

Lamp 

Ice 

Pictures 

Kentucky 

Iron 

Rough 

Square 

Fragrant 

Word 

Hear 

Bottle 

Water 

Top 

Hand 

Open 

Good 

Hand 

Milk 

Army 

Mountain 

Gold 

Wool 

Fruit 

Arm 

School 

Bees 

Floor 

Birds 

Fly 

Loud 

House 

Carriage 

Fern 

Red 

Down 

Chair 

Ice 

Knife 

Tuesday 



30 The Interrelations of Mental Abilities 

in order to make the time limits as abrupt for triads 25 and 50 
as for any other. 

Method of Scoring. One mark was allowed for each correct 
response. The highest possible score for each series is 50 marks. 

£7 & E8 Mixed Relations. Two Series 

The time for these tests was 9 minutes each. 

Source. An extension of the Woodworth- Wells test by Dr. 
E. L. Thorndike. Woodworth and Wells (1911, p. 64). 1 

Description. These are in general similar to tests E5 & E6. 
Each series contains 40 groups of words. 

Presentation. To each pupil was given a sheet of paper con- 
taining the forty groups of words. Opposite each group was 
a blank space large enough to hold the fourth word. At the 
top of each paper of each series instructions were printed thus : 
"Write in each line a fourth word that fits the third word in that 
line in the way that the second word fits the first, as shown in 
the first three lines." 

color — red name — John 

page — book handle — knife 

fire — burns soldiers — fight 

The presentation of these two series differs from the presenta- 
tion of tests E5 & E6 in that in these two it was wholly visual 
while in tests E5 & E6 it was oral and auditory. Test E7 was 
given in February and test E8 was given in April. 

Method of Scoring. One mark was given for each correct 
response. The highest possible score for each series is 40 marks. 

Eg & 10 Reading Tests. Tzvo Series: Alpha and I, J, K, L 

The time allowed was as follows : — Alpha, 30 minutes ; I, 5 ; 
J, 10; K, 10; L, 15. 

Source. Test E9 is Thorndike's original Scale Alpha (not 
the well-known Alpha 2), for Measuring the Understanding of 
Sentences. Test Eio consists of similar material but much 
harder to read, and is designated I, J, K, L. (Sept. 1914, pp. 44. 
60-64 ). 2 

^Psychological Review Monographs, vol. 13, 1911. 
*Teachers College Record, September, 1914. 



The Tests and Their Administration 31 

Description. Scale Alpha (Test E9) has four paragraphs (the 
third and the fourth being the same), after each of which some 
questions are asked. Scales I, J, K, L have each one paragraph 
and are followed by five, seven, eight, and eight questions 
respectively. 

Presentation. Test E9 was given in February. Test Eio was 
given at one time in April. Above each paragraph instructions 
are given thus : "Read this and then write the answers. Read it 
again as often as you need to." 

Method of Scoring. Each correct answer received two marks ; 
each answer nearly but not quite correct received one mark; 
other answers received no mark. The highest possible scores are 
Alpha 32 and I, J, K, L 56. 

En & E12 Directions V 

The time for this test was 5 minutes. 

Source. This test is by Dr. Thorndike (Sept. 1914, p. 38). x 

Description. Ten commands are given to the pupils to be 
executed by them with a pencil on the given sheet of paper. 

Presentation. The pupils were told that this was a Directions 
test and were asked to follow the printed instructions. Extensive 
explanations were unnecessary since the pupils had had experience 
with this sort of test. The same test was given twice but on 
different days. 

Method of Scoring. One mark each was given for a correct 
response to Directions 1, 2, 3, 4, 8. Two marks each were given 
for a correct response to Directions 5, 6, 7, 9, 10. If one of these 
five was not wholly right but more than half right, one mark 
was given for it. The highest possible score is 15 marks. 

E13 & E14 Visual Vocabulary 

The time for this test was 30 minutes each. 

Source. This test is Thorndike's original Reading Scale A, 
Visual Vocabulary (not the well-known Reading Scale A2, Visual 
Vocabulary) (Sept. 1914, p. 3). 

\Loc. cit. 



2,2 The Interrelations of Mental Abilities 

Presentation. This test was given twice. The instructions 
are printed at the top of each paper: "Look at each word and 
write the letter F under every word that means a flozver," etc. 

Method of Scoring. This was in terms of penalties. Score = 
Errors-|-Omissions. For the purpose of comparison with the 
other tests the deviations from these marks had their positive 
and negative signs transposed. The plus signs were made minus 
and the minus signs were made plus. The highest possible merit 
score is 43 marks. 

E15 & E16 Visual Vocabulary. Two Series: XII and VIII 

The time for each series is 25 minutes. 

Source. These two tests are by Thorndike (Sept. 1914, pp. 27 
and 29). 

Description. These are similar to tests E13 and E14 except 
that only four rubrics are used. Test E15 (XII) has 104 words. 
Test E16 (VIII) has 100 words. These words are not arranged 
in groups and only roughly in the order of difficulty. 

Presentation. Instructions are printed at the top of each 
sheet similar to tests E13, E14 and E17. 

Method of Scoring. Same as in tests E13 and E14. The 
highest possible merit score is 104 marks for test E15 and 100 
marks for test E16. 

Eif Visual Vocabulary IX 

The time for this test is 15 minutes. 

Source. This test is by Thorndike (Sept. 1914, p. 27). 

Description. This test is similar to E13, E14, E15 and E16. 
One hundred and thirty words are given. These differ widely 
in degree of commonness ; only four rubrics are used. 

Presentation. This is the same as for tests E13, E14, E15, 
and E16. 

Method of Scoring. One mark was allowed for each word 
correctly denoted. The highest possible score is 130 marks. 

E18 Directions VII 
The time for this test is 10 minutes. 



The Tests and Their Administration 33 

Source. This test is by Thorndike. Nothing has hitherto 
been published upon it. 

Description. Twelve commands are given to the pupils to be 
executed by them with pencils on the given paper. The fulfillment 
of the commands depends on the knowledge of certain words. 

Presentation. The pupils were told that this was a Directions 
test and were asked to follow the instructions which were printed 
at the top of the sheet. 

Method of Scoring. Same as in tests E13 & E14. The highest 
possible merit score is 54 marks. 

Two samples (21 the easiest and 32 the hardest) of the ques- 
tions are given below : 

Do what it says to do. 

21. Show by a cross which costs most : an orange a suit of 

clothes a pair of skates a pound of sugar 

32. Show by a cross each word that means "to make clear" or some- 
thing like "to make clear" : 

execrate expound 

clarify traduce 

elevate extort 

satisfy explain 

elucidate antipathy 

Group F. Logical Tests 
Fi & F2 Faulty Arguments. Two Series 

The time for each of these is 5 minutes. 

Source. These are tests No. 37 and No. 39 Briggs (1913, 
PP- 34-35) - 1 

Description. Each series consists of four arguments. Three 
of these are invalid and one is valid. 

Presentation. At the top of each sheet are given instructions 
thus: — "Some of these arguments are faulty. Find each one 
that is unsound and in the blank space below it briefly tell why." 
These instructions were supplemented by some oral explanations. 

Method of Scoring. One mark was given for each fallacy 
explained. If the valid argument was left untouched and the 
others were attempted one mark was given for it. The highest 
possible score for each series is 4 marks. 

1 Loc. cit. 



34 The Interrelations of Mental Abilities 

.Fj & F4 Catches. Two Series 

The time for F3 is 5 minutes and for F4 is 6 minutes. 

Source. These are tests No. 41 and No. 42 Briggs (1913, 
P- 36). 

Description. Each series consists of five statements, each of 
which contains some impossibility. 

Presentation. At the top of each sheet are given instructions 
thus: "In each of the following sentences there is a 'catch.' 
Tell where the nonsense in each case is." These instructions 
were supplemented by some oral explanations. 

Method of Scoring. In F3 for each nonsensical sentence ex- 
posed, one mark was given. In F4 one mark each was allowed for 
1, 2, and 5, and two marks each for 3 and 4. The highest possible 
score for F3 is 5 marks and for F4 is 7 marks. 

The Statistical Treatment of the Scores 

1. The tests were in general treated as six groups according 
to the similarities of the tests. 

Group A. Mechanical or Motor or Constructive. 

Group B. Non-Verbal Spatial Relations. 

Group C. Non-Verbal Computational. 

Group D. Arithmetic stated in words. 

Group E. Very Verbal. 

Group F. Logical. 

These names are not adequately descriptive, nor, in the case of 
F, exactly appropriate, but are used for convenience. All that 
is implied by any one of them is the reference to the group of 
tests themselves. Words, for example, are involved to some 
extent in the so-called Test of Non-Verbal Spatial Relations; 
the tests of Diagram Matching and Diagram Drawing are not 
so strictly mechanical or constructive as the Assembling tests. 
The grouping, however, is probably the most significant single 
grouping to make. From data to be given later in this monograph, 
a critic may regroup in any desired way. 

2. The records of the two sexes have been kept apart and 
treated separately. 



The Tests and Their Administration 35 

3- Every test in a given group has been correlated by the 
Bravais-Pearson "product-moments" method (formula d) with 
every other test in that group. The record of every pupil who 
was present in both the tests to be correlated, was retained. The 
record of a pupil who was absent from one or both the tests, 
was omitted. For these correlations see Tables 49 to 56. 

4. These correlations have been modified for attenuation by the 
formula (e), that is, using geometrical averages or when negative 
correlations made the use of geometrical averages impossible by 
the formula (/), that is, using the arithmetical averages. Though 
the geometrical average is always smaller than or equal to the 
arithmetical average, yet a modification for attenuation by the 
geometrical average is not necessarily smaller than a modification 
made by the arithmetical average, since the difference between 
the two denominators may be equal to, or greater than, the differ- 
ence between the two numerators. For these modified correla- 
tions see Tables 57 to 62. 

5. The Average Deviations for each test were calculated and 
the sum of the average deviations for both parts of each pair 
for both sexes was found, and this sum was employed as a basis 
of calculation for the weights to be allowed for each test in 
the composites. One exception was made. The sums of the 
average deviations of tests E17 and E18 were computed sep- 
arately. For these average deviations and their sums and the 
weights allowed see Table 13. 

6. Six Composite Scores for each individual have been com- 
puted, weight being given as above described. 

7. The correlations of these composites one with another have 
been computed. See Tables 5 and 6. 

8. These correlations have been modified for attenuation. See 
Table 65. 

9. Each group of correlations has been tabulated in rows and 
in columns. 

10. Each column of the raw correlations of the composites 
for the boys has been correlated with every other column. The 
same procedure has been followed for the girls. The correla- 
tions (Rab) are given in Tables 20 and 21. 

11. Each of these correlations (Rab) has been corrected by 
Spearman's formula (/) and these corrected correlations (R'ab) 
are given in Table 28. Concerning these formulae (rab, Rab, and 



36 The Interrelations of Mental Abilities 

R'ab) Dr. Spearman writes (1914, p. 109): "The significance 
of Rab is by no means confined to the present problem. In par- 
ticular, its relations to rab are most interesting: the one may 
easily be positive when the other is negative, or vice versa. For 
many purposes, Rab seems to be the more important value of the 
two. . . . The question arises, whether or not the coefficients 
should be corrected for 'attenuation' before calculating Rab. 
The matter is simplified by the easily demonstrable fact that if 
Rab is = 1 for the corrected coefficients, it must be so for the 
uncorrected ones also, and vice versa. And even if Rab has 
any other value, it will not in general be appreciably modified 
by correcting for 'attenuation' (the statement sometimes made 
that the hierarchy tends to be much better for uncorrected than 
for corrected coefficients is erroneous). The correcting process 
has the disadvantage of greatly complicating equation R'ab." 

Formulae 
m = a measure of an individual in a test. 

n = the number of individual w's in a group. 

S or 2 = Summation. 
A = Arithmetic average. 

x or y = the deviation of any m from A. 
A. D. = Average Deviation from A. 
S.D. or a r= Standard Deviation. 
r = Correlation according to the "Product-moment" 

method. 
P. E. = Probable Error, or Sampling Error : used only when 

an inference is drawn from the particular to the 

general. 
Rab = The Correlation of the respective correlations in 

two columns. 
R'ab — Rab corrected for the Sampling Errors of pax and 

pbx by the Spearman formula (/). 
pax — Deviation of each value of rax from the mean of rax. 

pbx — Deviation of each value of rbx from the mean of rbx. 

Sax = P.E. of rax. 

S,bx = P.E. of rbx. 

a 2 ax — mean value of ~2, 2 ax -— .6745 2 . 

a 2 bx = mean value of 'Sfbx -4- -6745 2 . 

aax abx = mean value of ^ax "Sbx -4- -674s 2 . 



The Tests and Their Administration $y 

Formulae 
Arithmetic Average = ^,mn r a \ 

A.D. = Arithmetic %x\n or Arithmetic %yln (h) 

o or S.D. = ^ 5Z or V3Z or Vl*^_ A . r , 

_ S(+^)-2(-^) o^, — g».--o », ... 

r *i/ — — , or ± (d) 

\|2(^ 2 )— 2(y) 2a^ 

Modifying formula forf r ~ „ „ 

,. , • • I -,4 ' »1 2/1 " ' X\ 2/2 * ' X2 VI ' ' XS 2/2 /- \ 

attenuation using geo-y *v — ^~ — (e) 

metrical averages [ (^*i*2 • r y\yv 

Modifying formula for] *- ,~ _■_ ~ . „ 

attenuation using anth- >* *v — — -^- (/) 

metical averages J ^(^1^2 + ^2/12/2) 

„ , .6745(1— r 2 ) 

P.E.ofr=± ^ ( ^ 



\T* /.6745 

—P. E.r) (/t) 



.6745 \V^~ 

p S(Pqs P frr) ... 



p , _ ^(PaxPbx) — hi— 1) r ab <J ax ff hx 

M ) 2(p 2 a *) - (»- \)*\ x \ \ %(p\ x ) - („_ l)^f 

15 tt -6745 

(0 

pg r=PF PF -6745a- distribution 

average true average obtained average \j n 



SECTION II 

THE NATURE OF THE ABILITIES MEASURED : THE 
INTERRELATIONS OF THE SEVERAL TESTS 

The Manipulative or Mechanical Tests 

The abilities measured by the Manipulative tests are not by 
any means identical. The notes which follow are based upon 
Tables I and 2. All correlation numbers are hundredths. 

Tests Ai & A2 (Stenquist Construction or Assembling Test) 
require synthetic ability. The subject must be able to pick up 
two or more pieces and to combine them, without any pattern, 
into a workable whole. Symbols of all kinds are omitted. The 
subject may succeed with some of these devices by the method 
of trial and error, but he is much more likely to succeed if he 
recognizes the device and knows its use and the way it looks 
when it is properly united. The average correlations of this pair 
with the other Manipulative tests, excluding handwriting, are 
only +25 (raw) and only -f-47 (modified), while the average 
reliability coefficient is +49. Assembling correlates with one 
of the other half as well as it does with itself. 

Tests A3&A4 (Recognition of Mechanical Devices) require 
some knowledge of names, some knowledge of mechanical de- 
vices, and some slight ability to reach a conclusion by the method 
of exhaustion. This pair does not require any motor or manipu- 
lative skill. The average correlations of this pair with the other 
members of the group, excluding handwriting, are only +19 
(raw) and only +33 (modified), while the average reliability 
coefficient is +59. It correlates with one of the others only one 
third as well as it does with itself. 

Tests A$ & A6 (Knot Making) require synthetic ability. The 
subject does not need any knowledge of words, but he must be 
able to understand a pattern and to apply the pattern to concrete 
substances. He needs also some power of visual imagery and 
some manual dexterity. The average correlations of this pair 
with the other members of the group, excluding handwriting, are 
only +31 (raw) and only +50 (modified), while the average 
reliability coefficient is +65. It thus correlates with one of the 
others about half as well as it does with itself. 



Interrelations of the Several Tests 



39 



TABLE 1— INTERRELATIONS OF THE MANIPULATIVE TESTS 

Averages of Boys' and Girls' Average Raw Correlations 
Stenquist 

Construe- Recogni- 
tion or tion of Diagram Diagram Hand- 
Assem- Mech- Knot Metal Match- Draw- writ- 
bling anisms Making Puzzles ing ing ing 
A1&A2 A3&A4 A5&A6 A7&A8 A9&A10 A11&A12 A13&A14 

Al & A2 30 30 27 27 12 —22 

A3 & A4 30 .. 15 22 14 16 —16 

A5 & A6 30 15 .. 22 39 48 —20 

A7 & A8 27 22 22 .. 22 14 —02 

A9 & A10 27 14 39 22 .. 32 03 

All & A12 12 16 48 14 32 .. —05 

126 97 154 107 134 122 —62 

Averages 25 19 31 21 27 24 —10 

A1&A2 A3&A4 A5&A6 A7&A8 A9&A10 A11&A12 A13&A14 
Reliability 

Coefficients... 49 59 65 32 52 80 64 

TABLE 2— INTERRELATIONS OF THE MANIPULATIVE TESTS 
Averages of Boys' and Girls' Correlations Modified for Attenuation 

A1&A2 A3&A4 A5&A6 A7&A8 A9&A10 A11&A12 A13&A14 

Al & A2 57 50 63 50 16 —36 

A3 & A4 57 .. 22 44 24 18 —24 

A5 & A6 50 22 .. 46 70 64 —30 

A7 & A8 63 44 46 .. 46 25 —04 

A9 & A10 50 24 70 46 .. 49 12 

All & A12 16 18 64 25 49 .. —07 

236 165 252 224 239 172 —89 

Averages 25 19 31 21 27 24 —10 



Tests Aj & A8 (Puzzles) require analytic ability. The subject 
does not need any knowledge of words more than that required 
to understand instructions. He does not need to know the 
purpose of the devices, in fact they have none except to perplex 
him. The simpler puzzles may be solved by merely fumbling 
with them, but the more complex puzzles require some insight 
into their construction. The subject does not need any knowledge 
of patterns or of mechanical instruments. He can clearly see the 
whole of each component part. He needs to know only the 
method by which the parts can be separated. The puzzles of 
the three graduated series measure, to some extent, the subject's 
learning ability, since if he recognizes the principle underlying 
the first puzzle in a graduated series and can use to advantage 
this knowledge, he will find the succeeding puzzles much simpler 
than they otherwise would be. If he fails to recognize the 
principle then he must proceed under increasing difficulties as 
the puzzles become more complicated. The average correlations 
of this pair with the other members of the group, excluding 



40 The Interrelations of Mental Abilities 

handwriting, are only -f-2i (raw) and only -(-45 (modified), 
while the average reliability coefficient is +32. This is much 
the lowest reliability coefficient of the group. Its smallness is 
due probably to the element of chance which enters so largely 
into all kinds of puzzle tests. This reliability coefficient agrees 
closely with the findings of Burt and Moore (1912, p. 375), * who 
report a reliability coefficient of -(-30 for wire puzzles. The 
test thus correlates two thirds as well with one of the others 
as it does with itself. 

Tests A9&A10 (Diagram Matching) require analytic ability. 
The easiest method of procedure is to isolate the essential part 
of the whole diagram and to match it with the given quarter. 
The tests require ability to recognize identities and to carry a 
spatial scheme in mind. The subject does not need any knowl- 
edge of words beyond that required to understand instructions. 
Of the arabic numerals he needs merely enough knowledge 
to enable him to write the identification numbers. The average 
correlations of this pair with the other members of the group, 
excluding handwriting, are only — j— 27 (raw) and only -(-48 
(modified), while the average reliability coefficient is -(-52. This 
test thus correlates half as well with one of the others as with 
itself. 

Tests An & A12 (Diagram Drawing) require synthetic ability. 
The subject must be able to understand and to follow a pattern 
and to carry a spatial scheme in mind. A knowledge of words 
beyond the instructions is unnecessary. The average correla- 
tions of this pair with the other members of the group, excluding 
handwriting, are only -f-24 (raw) and only +34 (modified), while 
the average reliability coefficient is -j-80. This very large re- 
liability coefficient is due probably to the very large average 
deviations, which are larger than any others in the whole investi- 
gation except tests E7 & E8, and also to the fact that both 
chance and practice have but little effect on the subjects' scores. 
This test thus correlates less than one third as closely with one 
of the other tests as it does with itself. 

Tests A 13 & A14 (Handwriting) require a highly complex 
form of motor activity and coordination of the arm, of the wrist, 

1 "The Mental Differences Between the Sexes," Journal of Experi- 
mental Pedagogy, 1912. 



Interrelations of the Several Tests 41 

of the fingers, of the eyes, and of the cerebro-spinal system. 
The exceeding complexity of handwriting can be perceived by 
right-handed persons if they will endeavor to write with the 
left hand. These tests require some, but not an accurate knowl- 
edge of spelling, since the subjects were not penalized for mis- 
spelled words. They require ability to transmute sounds into 
legible symbols, and to make these symbols clear, even, and 
beautiful. The average correlations of this pair with the other 
members of the group are ■ — 10 (raw) and — 15 (modified), 
while the reliability coefficient is -{-64. This is the highest 
reliability coefficient in the croup except An and A12 which is 
-f-80 and A5 and A6 which is -{-65. Handwriting as tested is thus 
nowise a symptom of the sort of ability required to assemble 
mechanisms tie knots or dismember puzzles. 

The low average correlations, apart from handwriting, the 
highest raw being —f-31 and the highest modified being +50, 
indicate that the functions involved in any one test are not 
identical with the functions involved in the other tests. This 
is especially true of the handwriting, the correlations of which 
indicate not only that the functions are different, but that they 
are somewhat incompatible. 

The Spatial Relations Tests 

The notes which follow are based upon Tables 3 and 4. Much 
more extended tests are needed before anything certain can be 
inferred about the community of these tests. So far as these 
results go it is slight. Because of the low correlations of the 
two halves of the Locus test one with another, and of the test 
for Similar Figures with the test for Congruent Figures, the 
modifications for attenuation are subject to very large probable 
errors. 

Tests Bi & B2 (Rhombuses). The average correlations of 
this pair with the other members of the group is only +10 (raw) 
and only -(-28 (modified), while the average reliability coefficient 
is +58. 

Tests B3 & B4 (Locus) seem to demand selective thinking 
with spatial relations and a knowledge of words and of some 
well-known objects : canal, boat, watch, circles, parallel straight 



42 



The Interrelations of Mental Abilities 



TABLE 3— SPATIAL RELATIONS 



TABLE 4— SPATIAL RELATIONS 





TESTS 






TESTS 




Averages of Boys' and of Girls' 
Average Raw Correlations 

Matching 
Similar and 
Rhombus Locus Congruent 
Tests Tests Figures 


Averages of Boys' and of Girls' 

Correlations Modified for 

Attenuation 

Matching 
Similar and 
Rhombus Locus Congruent 
Tests Tests Figures 




B1&B2 


B3&B4 


B5&B6 


B1&B2 


B3&B4 


B5&B6 


B1&B2 
B3&B4 
B5&B6 


14 
05 


14 
08 


05 
08 


34 
21 


34 

47 


21 
47 




19 


22 


13 


55 


81 


68 


Averages : 


10 
B1&B2 


11 

B3&B4 


06 

B5&B6 


28 


40 


34 


Reliability 
Coefficients 58 


22 


04 









lines, pencil, string, helix, scissors, curves, points of the com- 
pass, houses, roads. The average correlations of this pair with 
the other members of the group are only — (— 1 1 (raw) and only 
-f-40 (modified), while the average reliability coefficient is only 
-f-22. This low reliability coefficient is probably due to the in- 
trinsic difficulty of the test. With some 150 high school girls 
Miss Rogers obtained a reliability coefficient of only +05. 

Tests B5 & B6 (Applying Definitions of Similar and of Con- 
gruent). Understanding of the definitions given for "Similar" 
and for "Congruent" and recognition of similarities and of dif- 
ferences in form are the essential requirements. The average 
correlations of this pair with the other members of the group 
are only -j-06 (raw) and only +34 (modified), while the average 
reliability coefficient is only -f-04. 



Arithmetical Tests — Computation 

Each of these eight tests requires some addition, some subtrac- 
tion, some multiplication and some division, although tests C3 & 
C4 are primarily concerned with addition, tests C5 & C6 with 
subtraction, and tests Cy & C8 with division. Tests C3 to C8 
are alike in that they require no ability in reading words and do 
measure stock arithmetical knowledge. 

Tests Ci & C2 should have been put in a group by themselves 
or in the D group, but this was realized too late. That these 
tests do not belong to this C group is clearly shown by their 



Interrelations of the Several Tests 



43 



TABLE 5— ARITHMETICAL TESTS: 
COMPUTATION 

Averages of Boys' and of Girls' Average 
Raw Correlations. 
"Catch Sub- 

Prob- Addi- trac- Divi- 
lems" tion tion sion 
C1&C2 C3&C4 C5&C6 C7&C8 

CI & C2 16 24 26 

C3 & C4... 16 .. 34 34 

C5 & C6... 24 34 .. 42 

C7 & C8... 26 34 42 



Averages 



66 

22 



28 



100 
33 



102 
34 



Averages, exclud- 
ing CI & C2 34 38 38 

C1&C2 
Reliability Coefficients 44 



TABLE 6— ARITHMETICAL TESTS: 
COMPUTATION 

Averages of Boys' and of Girls* Correla- 
tions Modified for Attenuation. 
"Catch Sub- 

Prob- Addi- trac- Divi- 
lems" tion tion sion 
C1&C2 C3&C4 C5&C6 C7&C8 

CI & C2 36 51 56 

C3 & C4... 36 .. 84 86 

C5 & C6... 51 84 .. 94 

C7 & C8... 56 86 94 



143 
Averages . . 48 

Averages, exclud- 
ing CI & C2 



206 
69 



C3&C4 
34 



85 

C5&C6 
49 



229 
76 



89 



236 
79 

90 



C7&C8 
40 



average correlations with the other members of the group, which 
are only -{-22 (raw) and only +48 (modified), while the aver- 
age reliability coefficient is -j-44. 

Tests C3 & C4 have average correlations of only -j-28 (raw) 
and only +69 (modified) with the other members of the 
group, while the reliability coefficient is only +34- If tests 
Ci & C2 are omitted from the group then the average correla- 
tions become +34 (raw) and -(-85 (modified). 

Tests C5 & C6 have average correlations of only -f-33 (raw) 
and -\-?6 (modified) with the other members of the group, while 
the reliability coefficient is only -{-49, though this is the highest 
reliability coefficient in the group. If tests Ci & C2 are omitted 
from the group then the average correlations become +38 (raw) 
and -f-89 (modified). 

Tests Cy & C8 have average correlations of only -(-34 (raw) 
and -\-?9 (modified) with the other members of the group, while 
the reliability coefficient is only +40. If tests Ci & C2 are omitted 
from the group then the average correlations become +38 (raw) 
and +90 (modified). 

A test in Addition, Subtraction or Division thus correlates 
almost as closely with one of the others as it does with itself. 



Arithmetical Problems: Verbally Stated 

• Even a cursory reading of these tests shows that their contents 
are very similar. This conclusion is supported by their correla- 
tions, which show that the difference between any two pairs is 



44 The Interrelations of Mental Abilities 

about the same as the difference between any other two pairs, 
and this statement is true whether the raw or the modified coeffi- 
cients are considered. All the average raw correlations are low, 
the largest is only +35 ; likewise all the average reliability coeffi- 
cients are low, the largest is only — j— 38. On the other hand, all 
the average modified correlations are very large, the smallest 
being +83 and their average being +98. The largest of these 
exceeds even unity, which condition is due to the small size of 
the reliability coefficients compared with the size of the cross 
correlations (e. g., Di & D3, Di & D4, D2 & D3 and D2 & D4). 

TABLE 7— ARITHMETICAL PROB- TABLE 8— ARITHMETICAL PROB- 
LEMS: VERBALLY STATED LEMS: VERBALLY STATED 

Averages of Boys' and Girls' Average Averages of Boys' and Girls' Correla- 
Raw Correlations tions Modified for Attenuation 

D1&D2 D3&D4 D5&D6 D1&D2 D3&D4 D5&D6 

DI & D2 38 30 DI & D2 104 83 

D3 & D4 38 .. 32 D3 & D4 104 .. 106 

D5 & D6 30 32 1)5 & D6 83 106 

68 70 62 187 210 189 

Averages 34 35 31 Averages 94 105 94 

D1&D2 D3&D4 D5&D6 

Reliability Coefficients 38 30 34 

Dr. Bonser's description of his tests (1910, p. 14) 1 may be 
applied to all these : "The problems in arithmetic test the mathe- 
matical judgment, in general that form of deductive reasoning 
most closely resembling the syllogistic movement of formal logic. 
The steps here involved are three: First, the analysis of the 
situation by which the essential features of the problem are con- 
ceived and abstracted; second, the recall of an appropriate prin- 
ciple to be applied to the abstracted problem, a search among 
various principles which may suggest themselves for the right 
one; and third, involved in the second, the inference, the recog- 
nition of identity between the known principle and the new situa- 
tion. While this process goes on as implicit, explicitly there 
are made the concrete applications in the resolution of the prob- 
lems. Clearly these are examples of deductive reasoning of the 
usual scientific type, involving data, principles, and inferences. 
The only element omitted is that of verification, which, by the 
nature of the tests, cannot here be brought out." 

1 Loc. cit. 



Interrelations of the Several Tests 



45 



Very-Verbal Tests 

All these tests are based essentially upon a knowledge of words 
and thus differ from many of the preceding tests. The notes 
which follow are based upon Tables 9 and 10. 

Tests Ei & E2 (Use of Grammatical Definitions) require a 
knowledge of grammar, the former especially of verbs and the 
latter especially of subject, predicate, adjective, adverb and modi- 
fiers. Ability to reason would be desirable, though the subjects 
in these tests probably preferred to respond under the influence 
of first impressions. The tests are far too short to measure the 
abilities concerned. The average correlations of this pair with 
the other members of the group are only -{-19 (raw) and -\~7$> 

TABLE 9— VERT VERBAL TESTS 

Averages of Boys' and of Girls' Average Raw Correlations 
Gram- 
mar Para- 
Use of Gram- Mixed Mixed graph Direc- Word Knowledge 

Defini- mar Rela- Rela- Read- tions . ' . 

tions Usage tions tions ing E11& E13& E15& E17& 

E1&E2 E3&E4 E5&E6 E7&E8 E9&E10 E12 E14 E16 E18 

El & E2 —04 26 20 25 22 19 30 12 

E3 & E4 —04 .. 16 09 —04 —03 02 12 08 

E5 & E6 26 16 .. 57 48 41 52 66 33 

E7 & E8 20 09 57 .. 36 24 41 46 26 

E9 & E10 25 —04 48 36 .. 26 32 46 24 

Ell & E12.... 22 —03 41 24 26 .. 26 30 14 

E13 & E14.... 19 02 52 41 32 26 .. 53 33 

E15 & E16.... 30 12 66 46 46 30 53 .. 34 

E17 & E18.... 12 08 33 26 24 14 33 34 

150 36 339 259 233 180 258 317 184 

Average 19 04 42 32 29 22 32 40 23 

E11& E13& E15& E17& 

E1&E2 E3&E4 E5&E6 E7&E8 E9&E10 E12 E13 E16 E18 

Reliability Co- 
efficients ... 08 31 76 74 37 52 64 72 16 



TABLE 10— VERY VERBAL TESTS 

Averages of Boys' and of Girls' Correlations Modified for Attenuation 

E11& E13& E15& E17& 

E1&E2 E3&E4 E5&E6 E7&E8 E9&E10 E12 E13 E16 E18 

El & E2 —10 60 48 120 73 62 80 192 

E3 & E4 —10 .. 28 15 —08 —07 04 22 80 

E5 & E6 60 28 .. 76 90 64 75 90 75 

E7 & E8 48 15 76 .. 66 40 58 62 58 

E9 & E10 120 —08 90 66 .. 57 61 86 84 

Ell & E12.... 73 —07 64 40 57 .. 46 48 44 

E13 & E14.... 62 04 75 58 61 46 76 85 

E15 & E16.... 80 22 90 62 86 48 76 .. 80 

E17 & E18.... 192 80 75 58 84 44 85 80 

625 124 558 423 556 365 467 544 698 
Averages .... 78 16 70 53 70 46 58 68 87 
Averages omit- 
ting E3 & E4 91 .. 76 58 81 53 66 75 88 



46 The Interrelations of Mental Abilities 

(modified), while the average reliability coefficient is only -f-08. 
The difference between the raw and the modified coefficients is 
due, of course, to the small size of the reliability coefficient. This 
is especially true when Ei & E2 and E17 & E18 are compounded 
by the formula (e), the denominator of the fraction being nec- 
essarily very small, and thereby making the value of the whole 
fraction very large. The low raw correlation may be due to 
the element of chance which enters largely into these tests and 
to the short space of time given for the replies. 

Tests E3 & E4 (Grammatical Usage) require a knowledge of 
grammar, both etymological and syntactical, both of abstract rules 
and of concrete examples. Reasoning ability might, therefore, 
determine very largely the response, yet many of the pupils seem 
to have marked as correct those forms which they were in the 
habit of using or which they had often heard approved. The 
average correlations of this pair with the other members of the 
group are only -f~°4 (raw) and only — |— 16 (modified), while the 
reliability coefficient is only +31. The average raw and the aver- 
age modified correlations are the lowest in this whole group, while 
the average reliability coefficient is much lower than all the 
others except two: Ei & E2 and E17 & E18. The very low 
raw correlation may be due to the element of chance, which 
enters largely into it. The lowness of both the raw and the 
modified correlations may be due also to the ambiguity of cer- 
tain of the replies as signs of intellect. Expert teachers of Eng- 
lish composition are not unanimous in their opinions concern- 
ing some of the forms, therefore answers which some teachers 
would mark correct, others would mark incorrect. 

Tests £5 & E6 (Mixed Relations) have comparatively a high 
average correlations with the other members of the group: -f-42 
(raw) and -f-70 (modified), while the reliability coefficient -f— 76 
is the highest in this group. Tests Ey & E8 (Mixed Relations) 
have only moderately high average correlations with the other 
members of the group: +32 (raw) and -(-53 (modified), while 
the reliability coefficient +74 is next to the highest in the group. 
The difference between the correlations of the two pairs may be 
due to the fact that tests E5 & E6 were given orally and the 
time allowed for each quartette was the same. The tests thus 
given are more difficult than when given visually, as were tests 



Interrelations of the Several Tests 47 

Ey & E8, and when the time for the whole, but not for each 
quartette, is limited. The element of chance has but little influ- 
ence on this kind of tests. 

Tests Ep & Eio (Paragraph Reading). The average correla- 
tions of this pair with the other members of the group are mod- 
erately high: +29 (raw) and -f-70 (modified), while the relia- 
bility coefficient is only -f-37. The element of chance enters but 
slightly into these tests. 

Tests En & E12 are a test of sentence reading plus care in 
performing simple clerical operations. The test is very short 
and has a reliability coefficient of only +52 between the two 
trials, three months apart. It correlates with the two tests of 
paragraph reading about two thirds as clearly as they do one 
with the other. The averages of its correlations with the other 
tests in the group are +22 (raw) and +46 (modified). 

Tests E13 & E14, E15 & E16 and E17 & E18 are all tests of 
word knowledge. Tests E13 & E14 have eight rubrics, tests 
E15 & E16 and E17 have four rubrics, and test E18 uses the 
method of checking synonyms, together with that of choosing 
words of stated properties. The interrelations of these tests with 
each other and with all the others save the tests in Grammatical 
Usage E3 & E4 are, as shown in the tables, fairly close. 

In general, Tables 9 and 10 give evidence that Word Knowl- 
edge and Paragraph Reading are clearly correlated, but that a 
knowledge of correct usage (if the Starch Scale tests such) is 
much less clearly related to them than they are to each other. 
A difference in the difficulty of the paragraphs to be read or in 
the varieties of words to be classified seems to reduce correla- 
tion measurably from unity, but the probable errors of all the 
coefficients are too large to make this indubitable. 

Tests Fi & F2 (Faulty Arguments) and Fj & F4 (Catches) 
require ability to perceive and to explain fallacies. They require 
a knowledge of facts, a practical though not a theoretical knowl- 
edge of the syllogism, and some subtlety of thought. These four 
tests are probably somewhat too difficult for pupils of the sixth 
grade. Moreover, they would be better if more questions were 
added, thus having four times as many tests, or if each paper 
were four times as long. The average correlations between the two 



4 8 



The Interrelations of Mental Abilities 



Logical Tests 



TABLE LI— LOGICAL TESTS 



TABLE 12— LOGICAL TESTS 



Averages of 
age 


Boys' and of Girls' Aver- 
Raw Correlations 


Averages 
lations 


of Boys' and 
i modified for 


of Girls' Corr*- 
Attenuation 


Faulty 
Arguments 


Catches 




Faulty 
Arguments 


Catches 


Fl & F2 
F3 & F4 


F1&F2 
26 


F3&F4 
26 




F1&F2 
90 


F3&F4 
90 




26 


26 




90 


90 


Averages 


26 


26 




90 


90 


F1&F2 
Reliability 
Coefficients 31 


F3&F4 
16 









pairs are +26 (raw) and +90 (modified), while the average 
reliability coefficient of tests Fi & F2 is +31 and of tests 
F3 & F4 +16. The low reliability coefficients accounts for the 
large difference between the raw and the modified coefficients. 



SECTION III 

THE COMPOSITE ABILITIES AND THEIR INTERRE- 
LATIONS 

All the #A Tests (Manipulative), except A13 & A14, were 
combined into two composite scores for each individual by multi- 
plying his deviation from the average for his sex in Ai & A2 by 
2, his deviation from the average of his sex in A3 & A4 by 6, and 
so on as shown in the table of weights below (Table 13). The 
Ai, A3, A5, Ay, A9, An products were added to form #Ai. 
The A2, A4, A6, A8, Aio, A12 products were added to form 
#A2, #Bi and #B2, two composite scores for each individual 
in all the B Tests (Spatial Relations) were formed similarly. 
Similarly for #Ci and #C2, #Di and #D2, #Ei and #E and 
#Fi and #F2. 

It will be seen in the table that all the tests within any one 
group are given about equal weight, with the following excep- 

TABLE 13— AVERAGE DEVIATION OF THE SEPARATE TESTS 















Multiplier used 


Approximate 














in obtaining 


Weight 




Boys 


Girls 


Total 


Composite Scores 


Attached 


AI &A2 


8.06 


7.72 


6.31 


5.84 


27.93 


2 


56 
46 
50 
44 
53 
62 


A3 &A4 


2.62 


1.97 


1.89 


1.16 


7.64 


6 


A5 &A6 


3.22 


4.20 


3.66 


5.41 


16.49 


3 


A7 &A8 


6.53 


5.08 


5.02 


5.12 


21.75 


- 


A9 &A10 


9 72 


3.88 


2.88 


3.88 


13.36 


4 
2 


A11&A12 


£77 


7.06 


6.51 


8.54 


30.88 


A13&A14 


12.14 


12.70 


10.47 


10.40 


45.71 






Bl &B2 


5.95 


5.92 


3.45 


5.75 


21.07 


1 
4 


21 
19 
21 


B3 &B4 


1.62 


1.27 


.75 


1.23 


4.87 


B5 &B6 


3.00 


1.91 


3.53 


2.10 


10.54 


- 


CI &C2 


1.09 


1.00 


.88 


.76 


3.73 


2 


8 

9 

10 

10 


C3 &C4 
C5 &C6 


2.25 
2.34 


2 22 
2i59 


2.31 
1.98 


2.16 
2.67 


8.94 
9.58 


1 
1 

1 


C7 &C8 


2.65 


2.39 


2.39 


2.22 


9.65 


D1&D2 


.97 


.80 


1.20 


1.05 


4.02 


1 
1 
1 


4 
4 
4 


D3&D4 


.97 


.88 


1.05 


.95 


3.85 


D5&D6 


1.19 


.89 


1.13 


.80 


4.01 


Bl &E2 
E3 &E4 
E5 &E6 
E7 &E8 
E9 &E10 
E11&E12 
E13&E14 
B15&E16 
B17 

&B18 


1.36 
3.52 
5.97 
7.19 
3.14 
2.57 
3.38 
8.00 
6.26 


1.43 

2 °3 
5i32 
9.73 
4.08 
2.12 
3.22 
5.31 

2.26 


1.19 

3.51 
5.71 
7.62 
3.07 
2 °° 
3.43 
8.04 
9.71 


1.51 
3.21 
5.14 
8.69 
5.02 
1.66 
3.28 
4.98 

2.09 


5.49 
12.47 
22.14 
33.23 
15.31 

8.57 
13.31 
26.33 
15.97 

4.35 


3 
3 
1 
1 
3 
1 
1 
1 
1 



16 
37 

22 1 

33 

45 

9 

13 1 
26 
16 

9J 


55 

■64 


Fl &F2 
F3 &F4 


.59 
1.36 


.63 
.81 


1.00 
1.35 


.86 
.75 


3.08 
4.27 


1 
1 


3 
4 





50 The Interrelations of Mental Abilities 

tions: Handwriting is given no weight at all. El & E2 (Under- 
standing and Use of Grammatical Definitions) are given about 
one quarter as much weight as E5 & E6 and E7 & E8 (Mixed 
Relations), E9 & Eio (Paragraph Reading) or E13 & E14, 
E15 & E16 and E17 & E18 (Word Knowledge), and half as much 
weight as the tests E3 & E4 (Usage). 

On the basis of present knowledge these weightings could be 
improved, as by the separation of Ci & C2 or by their transfer to 
the D group, and by attaching much less weight to E3 & E4. 

The correlations of the two composites of the same group 
were as follows : 

TABLE 14— IIBLIABILITY COEFFICIENTS OF THE COMPOSITE SCORES 







31 Boys 


38 Girls 


Average 






#A1 & #A2 




90 




77 


84 






#B1 & #B2 




55 




17 


30 






#C1 & #C2 




70 




69 


70 






#D1 & #D2 




56 




70 


63 






#E1 & #E2 




82 




80 


81 






#F1 & #F2 




39 




25 


32 






TABLE 15— AVERAGE RAW CORRELATIONS OF THE COMPOSITES 


Boys #A 


i£B 


#c 


#D 


#E #F 


Girls #A #B 


#C #D 


#E #F 


#A 


60 


24 


00 


30 —07 


15 


29 14 


31 08 


#B 60 




12 


03 


18 08 


15 


07 18 


21 19 


#C 24 


12 




51 


31 —25 


29 07 


60 


47 10 


#D 00 


03 


51 




22 —13 


14 18 


60 


59 26 


#E 30 


18 


31 


22 


32 


31 21 


47 59 


42 


#F —07 


08 


—25 - 


-13 


32 


08 29 


10 26 


42 


TABLE : 


L6— CORRELATION OF THE COMPOSITES 


MODIFIED 


FOR 










ATTENUATION 






Boys #A 


#B 


#c 


#D 


#E #F 


Girls #A #B 


#C #D 


#E #F 


#A 


86 


29 


01 


34 —11 


30 


29 19 


39 10 


#B 86 




18 


05 


25 16 


30 


14 50 


46 irs 


#C 29 


18 




80 


41 —11 


29 14 


86 


61 21 


#D 01 


05 


80 




31 —24 


19 50 


86 


79 57 


#E 34 


25 


41 


31 


49 


39 46 


61 79 


92 


#F —11 


16 


—41 - 


-24 


49 


10 128 


21 57 


92 


TABLE 17— 


AVERAGES 


OF 


THE BOYS' 


AND OF THE 


GIRLS' CORRELA- 






TIONS 


MODIFIED FOR ATTENUATION 




#A 


#B 


#c 


#D 


#E #F 








#A 


58 


L"j 


10 


37 00 








#B 58 




16 


28 


36 72 








#C 29 


16 




83 


51 —10 








#D 10 


28 


83 




55 17 








#E 37 


36 


51 


55 


71 








#F 00 


72 


—10 


17 


71 









When the Composite Scores are correlated, it appears that #C 
Arithmetical Computation and #D Arithmetical Problems, stated 
in words, are most akin; The Very- Verbal #E and the Log- 
ical #F tests are closely allied; the so-called Manipulative #A 
group and the Spatial Relations #B group are next most closely 



The Composite Abilities and Their Interrelations 51 

allied. Between the Manipulative #A group and the Logical 
#F group the correlation appears to be very low. The facts 
are given in Tables 15 and 16. The differences between the 
results for boys and those for girls show regrettably great unre- 
liability which attaches to even these results from the Composites. 
If we assume that the Boy-Girl division of the material is a 
random division, we have as a result of all the errors that have 
accumulated in correlating and modifying for attenuation, unre- 
liabilities attached to the final section of Table 17 as follows: 













TABLE 


18 












#A 




#B 




#c 




#D 


#E 




r 


P.E. 


r 


P.E. 


r 


P.E. 


r 


P.E. 


r P.E, 


#B 


58 


14 
















#c 


29 


00* 


16 


01 












#D 


10 


045 


28 


11 


83 


015 








#B 


37 


01 


36 


05 


51 


05 


55 


12 




#F 


00 


05 


72 


28 


—10 


155 


17 


20 


71 11 









TABLE 


19 








#A 




#c 






r 


P.E. 


r 




P.E. 


#c 

#D 
#E 


29 
10 
37 


small 
045 
01 


83 
51 




015 
05 



*This technical zero is not, of course, to be taken at its face value. 

If we leave out the Spatial Relations #B and Logic #F Com- 
posites, which have low coefficients of self -correlation, we have: 



r P.E. 

55 12 

These results are sound enough, perhaps, to justify the asser- 
tions (1) that the Mechanical and Diagram test ability is much 
less closely related to ability with numbers or ability with words 
than these are one with another; (2) that Arithmetical Problems 
of the sort used for the pupils in grade six are only slightly con- 
taminated by differences in ability to read words (55 vs. 51), 
(3) that such problems are a very unsafe test of general ability 
to reason, and (4) that the Verbal Composite is the best single 
representative of the whole set of Composites. 



SECTION IV 
THE HIERARCHY OF THE SPECIFIC INTELLIGENCES 

The writer had not the slightest intention of employing the 
data of this study as a criterion of Spearman's theory of intelli- 
gence until all the coefficients of correlation had been obtained. 
Then, perceiving that the material was well suited for such a 
study, he calculated the correlations of the correlational columns 
for the six Composites. He was wholly unbiased ; he cared noth- 
ing whether the unifocal theory was supported or discredited. 
Either result would have been equally satisfactory to him. 

Dr. Spearman writes (1904, p. 225) : "We must insist upon 
a precise quantitative expression derived impartially from the 
entire available data ; we must renounce adroit manipulation of 
tables and graphs, still further rounded into the required shape 
by ingenious argument; the whole of our experimentally gained 
figures must without any selective treatment simply of them- 
selves issue into one plain numerical value." The correlations 
used here correspond in every way to these requirements. 

The correlations of the correlations for the Composites go dead 
against the theory of a single factor as the explanation of the 
amounts of resemblance found amongst the six Composites abili- 
ties, whether the raw or the modified coefficients, the coefficients 
for one sex separately or the averages of the corresponding coeffi- 
cients for the two sexes, the most reliable or the less reliable col- 
umns are taken, the average correlation of the correlations is far 
below unity, being in general much nearer zero than unity. 

The data, underlying a study of the theory of the hierarchy, 
may be manipulated in various ways and the results obtained 
depend upon the method of manipulation which has been em- 
ployed. 

First Method: All the correlational columns of the raw com- 
posites have been correlated and the results have been tabulated 
and are given in Tables 20 and 2T. In this method no manipula- 
tion of any kind whatsoever has been practised. Every correla- 
tion, without any regard to the size of the coefficient, has been 
allowed full weight. The boys show 66 correlations, the total 
of the positive correlations being T.458. the total of the negative 



The Hierarchy of the Specific Intelligences 53 

TABLE 20— BOYS 

RAW CORRELATIONS OF THE COMPOSITE CORRELATIONAL COLUMNS 

Non-Verbal Verbal Very- 
Manipulative Spatial Arithmetic Arithmetic Verbal Logical 

#A1 #A2 #B1 #B2 #C1 #C2 #D1 #D2 #E1 #E2 #F1 #F2 

#A1 97 95 90 —03 14 —11 —23 —01 04 —01 01 

#A2.. 97 .. 89 87 10 14 —10 —18 —07 —02 —07 —16 

#B1 95 89 .. 94 —11 —04 —26 —56 —07 —09 09 —08 

#B2 90 87 94 .. —15 —03 —40 —47 —08 —15 03 —19 

#C1 —03 10 —11 —15 .. 91 91 83 —03 —02 —66 —69 

#C2 14 14 —04 —03 91 .. 77 82 -03 06 —58 —70 

#D1 —11 —10 —26 —40 91 77 .. 91 21 —02 —56 — i9 

#D2 —23 —18 —56 —47 83 82 91 .. 01 05 —56 —52 

#E1 —01 —07 —07 —08 —03 —03 21 01 .. 58 45 33 

#E2 04 —02 —09 —15 —02 06 —02 05 58 .. 31 60 

#F1 —01 —07 09 03 —66 —58 —56 —56 45 31 .. 76 

#F2 01 —16 —08 —19 —69 —70 —49 —52 33 60 76 



#A1. 

#A2. 
#B1. 
#B2. 
#C1. 

#C2. 
#D1. 
#D2. 

#E1. 
#E2. 
#F1. 
#F2. 



—66 —7 —53 118 394 313 462 414 486 439 342 102 

correlations being 853, and the average being +09. The girls 
show 66 correlations, the total of the positive correlations being 
!>963, the total of the negative correlations being 491, and the 
average being -f-22. The average for both sexes, -f-16, gives no 
evidence for the theory of the common factor. 

Second Method: The manipulation employed in this method is 
the combining of the correlations from #Ai and #A2, those 
from #Bi and #B2, etc., and the using of their averages. The 
results are given in Table 22. The boys show 15 correlations, the 
total of the positive correlations being 299, the total of the nega- 
tive correlations being 286 and the average being -j-oi. The girls 
show 15 correlations, the total of the positive correlations being 
509, the total of the negative correlations being 169 and the aver- 
age being -\-2^. The average for both sexes, +12, is as before 
against the theory of the Common Factor. 



301 


297 


287 


274 


275 


284 


280 


262 


158 


164 


164 


170 


—39 


—60 


—121 


—147 


—169 


—138 


—194 


—252 


—29 


—30 


—244 


—283 








TABLE 2] 


—GIRLS 














23 


—15 


03 


10 


02 


—12 


—24 


—02 


—12 


—22 


—17 


23 




—74 


06 


39 


30 


14 


02 


15 


04 


—16 


—50 


—15 


—74 




—39 


—37 


-—14 


—20 


—09 


30 


—11 


38 


50 


03 


06 


39 




—21 


—43 


03 


—16 


43 


05 


43 


56 


10 


39 


— 37 


—21 




98 


84 


81 


60 


72 


34 


—26 


02 


30 


-^14 


-^3 


98 




80 


79 


52 


69 


10 


—20 


—12 


14 


—20 


03 


84 


80 




95 


66 


85 


65 


02 


—24 


02 


—09 


—16 


81 


79 


95 




68 


84 


44 


10 


—02 


15 


30 


43 


60 


52 


66 


68 




77 


51 


26 


—12 


04 


—11 


05 


72 


69 


85 


84 


77 




45 


21 


—22 


—16 


38 


43 


34 


10 


65 


44 


51 


45 




50 


—17 


—50 


50 


56 


—26 


—20 


02 


10 


26 


21 


50 




38 


133 


157 


198 


478 


420 


494 


463 


488 


462 


380 


215 


-104 


140 


210 


80 


84 


107 


32 


49 





23 


38 


113 



54 The Interrelations of Mental Abilities 



TABLE 22— CORRELATIONS OF 


THE 


CORRELATIONS. 


FORMULA 


(O 








BOYS 










GIRLS 






Boys 


#A 


#B 


#c 


#D 


#E 


#F 


Girls #A 


#B 


#c 


#D 


#E 


#F 


#A 




86 


12 


20 


—59 


41 




—64 


46 


91 


09 


04 


#B 


86 




06 


—27 


29 


03 


—64 




—60 


—38 


—04 


78 


#c 


12 


06 




85 


—53 


—33 


46 


—60 




73 


81 


21 


#D 


20 - 


-27 


85 




17 


—14 


91 


—38 


73 




76 


30 


#E 


—59 


29 


—53 


17 




—73 


09 


—04 


81 


76 




—05 


#F 


41 


03 


—33 


—41 


—73 




04 


78 


21 


30 


—03 






TABLE 


23- 


CORRECTED BY DR. 


SPEARMAN'S 


FORMULA (») 






#A 


#B 


#C 


#D 


#E 


#F 


#A 


#B 


#c 


#D 


#E 


#F 


#A 






09 


30 


















#B 






04 




















#c 


09 


04 






















#D 


30 
























#E 


























#F 


68 


























TABLE 24— ARITHMETIC 


COMBINED RAW. FORMULA 


[r> 






#A 


#B 


#CD 


#E 


#F 






#A 


#B 


#CD 


#E 


#F 


#A 




86 


62 


—99 


37 








—56 


91 


49 


65 


#B 


86 




39 


16 


—11 






—56 




—18 


—19 


82 


#CD 


62 


39 




—50 


82 






91 


—18 




55 


77 


#E 


—99 


16 


—50 




—73 






49 


—19 


55 




—34 


#F 


37 


—11 


82 


—73 








65 


82 


77 


—34 





Third Method: The manipulation employed in this method is 
the same as that of the second method, only it proceeds farther 
and averages the correlations for the two Arithmetical Com- 
posites: C and D. The boys show io correlations with an aver- 
age of +09. The girls show 10 correlations with an average of 
-(-29, giving an average of -f-19 for the two sexes together. It 
will be observed that the elimination of the correlations between 
two identical or closely similar abilities does not raise the correla- 
tions of the columns toward the high values required by the 
theory of a common factor. Table 24. 

Fourth Method: Dr. Spearman lays down the standard (1912, 
p. 56) : "In order to attempt to estimate the correct correlation 
between the columns, it is required that in each of these columns 
the mean square deviation should be at least double the correc- 
tion to be applied to that deviation." And again he writes (1914, 
p. 112) : "Reject all pairs of columns, in either of which the sum 
of the squares of the probable errors exceeds one-fourth of the 
sum of the deviations from the average." This fourth method is 
in harmony with the above standard, otherwise it is the same as 
the first method. The columns and their correlations which 
remain are : 



The Hierarchy of the Specific Intelligences 



55 





TABLE 25 










Boys 








Girls 




r 


r 






r 




r 


#A1 & #A2 97 #B2 & #C1 


—15 


#A1 & # 


10 


#C1 & #D1 


84 


#A1 & #C1 —03 #B2 & #C2 


—03 


#A1 & 


#C2 


02 


#C1 & #C2 


81 


#A1 & #C2 14 #B2 & #D1 
#A1 & #D1 —11 #B2 & #D2 


-^0 


#A1 & #D1 


—12 


#C1 & #E1 


60 


—47 


#A1 & #D2 


—24 


#C1 & #E2 


72 


#A1 & #D2 —23 #B2 & #F1 


03 


#A1 & #E1 


—02 


#C2 & #D1 


80 


#A1 & #P1 —01 #C1 & #C2 


91 


#A1 & #E2 


—12 


#C2 & #D2 


79 


#A2 & #C1 10 #C1 & #D1 


91 


#A2 & 


#C1 


39 


#C2 & #E1 


52 


#A2 & #C2 14 #C1 & #F1 


—66 


#A2 & 


#C2 


30 


#C2 & #E2 


69 


#A2 & #D1 —10 #C2 & #D1 


77 


#A2 & #D1 


14 


#D1 & #D2 


95 


#A2 & #D2 —18 #C2 & #D2 


82 


#A2 & #D2 


02 


#D1 & #E1 


66 


#A2 & #F1 —07 #D1 & #F1 


—56 


#A2 & #E1 


15 


#D1 & #E2 


85 


#B1 & #C1 —11 #D2 & #F1 


—56 


#A2 & 


#E2 


04 


#D2 & #E1 


68 


#B1 & #C2 —04 




#C1 & 


#C2 


98 


#D2 & #E2 


81 


The Probable Errors fo 


r the 


single 


correlations of the Com- 


posites are as follows : 
















TABLE 










Formula (g) 








Formula (h) 




31 Boys 38 Girls 






31 Boys 


38 Girls 


r P.E. P.E. 


r 




P.E. 




r 


P.E. 


10 12 11 


Oto 


22 


12 




Oto 20 


11 


20 12 11 


23 to 


36 


11 




21 to 36 


10 


30 11 10 


37 to 


46 


10 




37 to 47 


9 


40 10 9 


47 to 


54 


9 




48 to 56 


8 


50 9 8 


55 to 


61 


8 




57 to 63 


7 


55 8 8 


62 to 


68 


7 




64 to 70 


6 


60 8 7 


69 to 


73 


6 




71 to 76 


5 


65 7 6 


74 to 


79 


5 




77 to 82 


4 


70 6 6 


80 to 


84 


4 




83 to 86 


3 


75 5 5 


85 to 


89 


3 




87 to 92 


2 


80 4 4 


90 to 


93 


2 




93 to 97 


1 


85 3 3 


94 to 


97 


1 




98 to 100 





90 2 2 


98 to 100 











95 11 














100 















The boys show 25 correlations, the total of the positive correla- 
tions being 479, the total of the negative correlations being 371, 
and the average being -f~°4- The girls show 26 correlations, the 
total of the positive correlations being 1,189, tne total of the 
negative correlations being 50, and the average being -}~44- The 
combined result is -f-24. 

Fifth Method: This is the same as the second method, except 
that the standard mentioned in the fourth method is employed. 
For the boys three columns and their correlations remain, the 
other twelve being excluded by the standard. These three are: 
#A & #C+i2, #A & #D+20, #B & #C+o6. The aver- 
age is +13. For the girls all the columns are excluded by the 
standard. 

Sixth Method: This is the same as the third method, except 
that the standard mentioned in the fourth method is employed. 
By this method all the columns for both boys and girls are 
excluded by the standard. 

Seventh Method: This is the same as the first method, except 







Girls 




—19 


#A1 & #C1 


13 


#C1 & #D1 


96 


00 


#A1 & #C2 


00 


#C1 & #D2 


93 


—59 


#A1 & #D1 


—19 


#C1 & #E1 


78 


—78 


#A1 & #D2 


—41 


#C1 & #E2 


84 


11 


#A1 & #E1 


00 


#C2 & #D1 


85 


104 


#A1 & #E2 


—05 


#C2 & #D2 


86 


106 


#A2 & #C1 


41 


#C2 & #E1 


57 


—85 


#A2 & #C2 


21 


#C2 & #E2 


74 


89 


#A2 & #D1 


08 


#D1 & #D2 


109 


113 


#A2 & #D2 


00 


#D1 & #E1 


75 


—77 


#A2 & #E2 


00 


#D1 & #E2 


97 


—88 


#A2 & #E1 


03 


#D2 & #E1 


81 




#C1 & #C2 


112 


#D2 & #E2 


95 



56 The Interrelations of Mental Abilities 

that both the standard and the formula (/) are applied. The 
columns and their correlations, which remain, are: 

TABLE 27 
Boys 

#A1 & #A2 102 #B2 & #C1 

#A1 & #C1 00 #B2 & #C2 

#A1 & #C2 14 #B2 & #D1 

#A1 & #D1 —13 #B2 & #D2 

#A1 & #D2 —32 #B2 & #F1 

#A1 & #F1 —01 #C1 & #C2 

#A2 & #C1 07 #C1 & #D1 

#A2 & #C2 07 #C1 & #F1 

#A2 & #D1 —10 #C2 & #D1 

#A2 & #D2 —24 #C2 & #D2 

#A2 & #F1 —10 #D1 & #F1- 

#B1 & #C1 —12 #D2 & #F1 

#B1 & #C2 00 

Twenty-five correlations remain for the boys. The total of 
the positive correlations is 553, the total of the negative correla- 
tions is 508, and the average is -\-02. Twenty-six correlations 
remain for the girls. The total of the positive correlations is 
1,308, the total of the negative correlations being 65 and the 
average being +48. The combined result, -f-25, is far from the 
approach to 100 required by the theory of the hierarchy, due to 
one common factor as the main cause of correlation. 

Eighth Method: This is the same as the second method, except 
that both the standard and the formula (/) have been applied. 
For the boys three columns and their correlations remain : 
#A & #C+o9, #A & #D+30, #B & #0+04. The total is 
-|-43, and the average is +11. For the girls all the columns are 
excluded. The evidence for the boys is against the hierarchy, 
and for the girls it is non-existent (Table 23). 

Ninth Method: This is the same as the third method, except 
that both the standard and the formula (/) are employed. All 
the columns for both the boys and the girls are excluded. 

Tenth Method: The manipulation employed in this method was 
the arranging in columns of the average raw correlations of boys 
and of girls for each Composite (Table 28), and then correlating 
these columns. The results are given in Table 29. 





TABLE 


28 




TABLE 29 


Average Raw Correlations of the Boys' 


Correlations of the eolumns of the 


and of 


the 


Girls' 


Composites 


Average Raw Correlations of the 












Boys' and of the Girls' 












Composites 


#A 


#B 


#c 


#D 


#E #F 


#A #B #C #D #E #F 


#A 


38 


26 


07 


30 00 


07 08 32 —73 36 


#B 38 




10 


10 


20 18 


07 —26 —70 —99 04 


#C 26 


10 




56 


39 —08 


08 —26 73 35 —02 


#D 07 


10 


46 




40 07 


30 —70 73 54 —08 


#E 30 


20 


39 


40 


37 


—73 —99 35 54 —71 


#F 00 


18 


—08 


07 


37 


36 04 —02 —08 —71 



The Hierarchy of the Specific Intelligences 57 

These correlations extend quite evenly from +73 to — 99. 
Table 30 shows 15 correlations, the total of the positive correla- 
tions being 249, the total of the negative correlations being 349, 
and the average being — 07. 

Eleventh Method: The manipulation used in this method was 
the arranging in columns of the average modified correlations of 
the boys and of the girls for each Composite (Table 30), and 
then correlating these columns; the results are given in Table 31. 
The correlations extend quite evenly from -(-68 to — 97. Table 
31 shows 15 correlations, the total of the positive correlations 
being -\-1g6, the total of the negative correlations being — 467, 
and the average being — 18. 

Twelfth Method: The writer applied to Table 28 the standard 
and the formula (/), but these excluded all the columns and 
their correlations. 

TABLE 30 TABLE 31 

Average Modified Correlations of the Correlations of the columns of the 

Boys' and of the Girls' Composites Average Modified Correlations of 

the Boys' and of the Girls' 



















Composites 








#A 


#B 


#c 


#D 


#E 


#F 


#A 


#B #C #D 


#E 


#F 


#A 




58 


29 


10 


36 


00 




—66 —01 19 


—93 


68 


#B 


58 




16 


28 


36 


72 


—66 


—97 —95 


24 


10 


#c 


29 


16 




83 


51 


—10 


—01 


—97 68 


—17 


—31 


#D 


10 


28 


83 




55 


16 


19 


—93 68 


07 


—18 


#E 


36 


36 


51 


55 




70 


—93 


24 —17 07 




—47 


#F 


00 


72 


—10 


16 


70 




68 


10 —31 —18 


—47 





It should be noted that the combination of the results reducing 
the sampling errors does not cause a closer approach to the -f-ioo 
required by the unifocal theory; nor does the use of correlations 
modified to offset the effect of the chance inaccuracies in the 
original measures. 

The correlations of the correlations for this group show no 
evidence of the unifocal theory, but on the contrary reveal a 
notable specificness in the abilities measured by the #A, #B, 
#C, #D, #E and #F groups. The question needs retesting 
with larger groups to reduce the sampling errors and with more 
extended tests to reduce the complexities of inference due to the 
low self-correlation coefficients. Spearman's use of the correla- 
tions of the correlations as a criterion of the nature of the 
organization of human faculty is most ingenious and important, 
but the actual working of his "standard" seems to cut out the 
columns with the low correlations and so the cases where specific- 
ness would be especially shown. 



SECTION V 

SEX DIFFERENCES 

These tests give results supporting the conclusion of recent 
years that the abilities of boys and of girls of like age are on 
the whole approximately equal, that the boys are better in dealing 
with mechanical contrivances and a little better in mathematics, 
while the girls are better in dealing with words and verbal rela- 
tions. The results may be stated most briefly in terms of per- 
centages of overlapping or in terms of the multiple of the varia- 
bility A or the score in question by which the boys' average sur- 
passes that of the girls. In this study the latter method has been 
chosen. With the results from the present investigation are 
recorded also the results from similar tests by Mrs. Woolley (H. 
B. Thompson), Thorndike, Rusk, Bonser, and Burt and Moore. 
These are shown in Tables 32 to 37. 



TABLE 32 Number 

Boys' of Separate 

Boys Boys' Average — Tests, in Which 

Exceed Average — Formulae Girls' One Sex Exceeds 

Girls Girls' (e) (b) Average the Other 

by Average P.E. A.D. A.D. Boys Girls Total 

li JeS)::::: 2.39 265 - 18 492 - 50 9 3 » 

II {Evensi::::: il 137 - 11 ** - 45 * 2 ■ 

#C (Odds) —.19 _26 .05 1.99 —.13 3 5 8 

#C (Evens) — .34 

#D (Odds). 41 35 05 99 .35 6 6 

#D (Evens) 28 

#E (Odds). 1.14 ln .03 4-37 2 5 12 6 18 

#E (Evens) 1.07 

#P (Odds). —.26 _ 18 -06 -92 _.20 4 4 

#F (Evens) —.09 

Handwriting ... ^?J? -10.54 .94 11.43 -.92 _0 J _2 

34 22 56 

Puzzles A7&A8.. 5.16 

—3.14 1.01 2.93 5.44 .19 

Analogies .54 

E5 to E8 1.40 .97 .30 6.92 .14 

TABLE 33 
Computed from Mrs. Woolley's data (1903, 109, 125) 50 students. 

Boys' Median— Ingenuity Tests -. 

Girls' Median #1 #2 #3 #4 #5 Physics Average 

A.D. —.13 +.32 +.62 +60 +.73 +.89 +.50 

TABLE 34 

Computed from Thorndike's data (Ed. Psych., Vol. Ill, 1914, page 183). 

Boys' Median — Associative and High School College 

Girls' Median Conceptual Processes Mathematics Mathematics 

A.D. —.06 .22 —.17 



Sex Differences 



59 



TABLE 35 
Computed from Miss Rusk's data (Thorndike, Ed. Psych., Vol. Ill, p. 184). 
Boys' Median — High School English High School Physics 

Girls' Median __ ,« 

A.D. — - 5o 60 

TABLE 36 
Computed from Dr. Bonser's data (1910). 

(Grades 4A to 6A) 
Boys' Median - Boys' Median- 

Girls' Median G lrls Median 

Average P.E. A.D. A.D. 

Mathematical 3.14 

Tabfe^VT 3.1 3.27 ± .44 6.21 .5a 

Page 25 1.5g 

Controlled —.15 

Association -39 _ .„ ^^ 

Table XIII -18 29 ± -08 3.43 .08 

Page 35 .71 

Controlled ~ i2m -n 

Association — 3.50 « in -k 

Table XX —5.25 —5.35 ±1.08 15.10 —.3D 

Page 42 — 4.58 

— 1.25 

Selective -51 

Judgment 1.90 -„ 

Table XXVI — 4.2o .20 ± .&J ».au .«a 

Page 52 4.00 

— 1.16 

TABLE 37 
Computed from Burt and Moore's data (1912, pp. 372-375) 

Boys' Median — Boys' Median — 

65 Liverpool Children : Girls' Median Girls' Median 

Addition 15 •** 

Multiplication ld -* 1 

130 Wallsey School Children: 

Wire Puzzles ... . . " '* 

Reconstructing Picture Blocks -» •»£ 

Reconstructing Picture Postcards —02 — .ov 

Analogies • ~ $ |? 

Completion of Arguments u < •**■ 

The average ages of the boys and of the girls are almost 
identical. 

TABLE 38 

Subjects in the Composites All the Subjects 

31 Boys 38 Girls 37 Boys 46 Girls 

Totals- 364. years 450. years 434. years 542. years 

Averages: 11.741 years 11.842 years 11.73 years 11.782 years 

The average marks of the two sexes obtained in the class- 
room examinations during February, March, April, May, and 
June in arithmetic, geography, history, grammar, composition, 
and spelling are almost identical: Boys' average marks, 79.874 
marks; and girls' average marks, 79.528 marks. Therefore no 
appreciable difference exists between these two groups so far as 
ages and scholastic attainments, as measured by class-room 
examinations, are concerned. 



60 The Interrelations of Mental Abilities 

If the average (see Sex Difference, Tables 33 to 38) be taken 
of excesses in the Manipulative Tests (#A), in Mrs. Woolley's 
Ingenuity Tests and Physics, in Miss Rusk's Physics and in Burt 
and Moore's Puzzles (wire, block, and postcard), it is +.50; 
that is, the boys exceed the girls by 50 per cent of one A.D. 

If the average be taken of excesses in the Mathematical Tests 
(#B and #C and #D), in Thorndike's high school subjects, in 
Bonser's Table VI, and in Burt and Moore's Addition and Multi- 
plication, it is +.27 ; that is, the boys exceed the girls by 27 per 
cent of one A.D. 

If the average be taken of excesses in the Reasoning Tests 
■(#D and #F) in Bonser's Tables VI and XXVI, and in Burt 
and Moore's Completion of Arguments, it is +.18; that is, the 
boys exceed the girls by 18 per cent of one A.D. 

If the average be taken of excesses in the English Tests (#E) 
and Miss Rusk's High School English, it is — .15 ; that is, the girls 
exceed the boys by 15 per cent of one A.D. 

If the average be taken of excesses in the Analogies E5 to E8, 
Thorndike's Associative and Conceptual Processes, Bonser's Con- 
trolled Association (Tables XIII and XX), and Burt and 
Moore's Analogies, it is — .13; that is, the girls exceed the boys 
by 13 per cent of one A.D. 

If the average be taken of excesses in the simple Arithmetic 
(#C) and in Burt and Moore's Addition and Multiplication, it is 
-(-.26 ; that is, the boys exceed the girls by 26 per cent of one A.D. 

If the average be taken of excesses in the Puzzle Tests A7 & 
A8 and in Burt and Moore's Puzzles (wire, blocks, and post- 
cards), and in Mrs. Woolley's Ingenuity Tests I, III, and IV, 
it is — f- .41 ; that is, the boys exceed the girls by 41 per cent of 
one A.D. 

In the handwriting the girls exceed the boys by 92 per cent of 
one A.D. 

In the Separate tests of this study (Table 32) the boys are 
superior in 34 tests and the girls in 22 tests out of 56. 

In the Composites the boys are superior in (#Ai), (#A2), 
(#Bi), (#B2), (#Di), (#D2), (#Ei) and (#E 2 ), while 
the girls are superior in (#Ci), (#C2), (#Fi) and (#F2). 



Sex Differences 61 

Sex Variability 

The variability of the boys is, on the whole, a trifle greater 
than that of the girls. The respective average deviations in the 
Composites are as follows : 

TABLE 39 

AVERAGE DEVIATIONS (WEIGHTED) OF THE COMPOSITES 

#A1 #B1 #C1 #D1 #E1 #F1 #A2 #B2 #C2 #D2 #E2 #F2 

Boys 56.5 12.0 7.41 2.32 33.3 1.67 53.2 10.4 6.93 1.87 31.8 1.35 

Girls 39.1 8.8 5.73 2.47 41.6 1.92 47.1 9.7 0.42 2.07 33.6 1.26 



SECTION VI 
INDIVIDUAL AND COMPOSITE SCORES 

Appended in Tables 40 and 41 are the original gross scores 
for each individual in each test and in Tables 42 and 43 are 
the Composite Scores devised by adding the weighted deviations 
as described on page 49. 

Appended in Table 44 are the averages for each sex in each test, 
and in Tables 45 to 48 the Reliability Coefficients or Correlations 
between the two trials of the same test, or two similar tests, and 
in Tables 49 to 56 the raw Correlations of each with every other 
test in its group, and in Tables 57 to 62 the correlations, modi- 
fied by Spearman's formulae (e and /) for Ai & A2 with A3 & 
A4, Ai & A2 with A5 & A6, and so on, and in Tables 63 and 64 
the raw correlations of the Composite Scores, and in Table 65 the 
modified Correlations of the Composites. 



Individual and Composite Scores 63 

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64 The Interrelations of Mental Abilities 



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66 The Interrelations of Mental Abilities 



TABLE 41— GIRLS' SCORES 



Girl 


Al 


A2 


A3 


A4 


A5 


A6 


A7 


A8 


A9 


A10 


All 


A12 


A13 


A14 


1 


11 


9 


7 


5 


2 


7 


25 


20 


11 


8 








188 


211 


2 


27 


28 


4 


3 




13 


24 


20 


18 


20 




15 


216 


208 


3 


9 


2 


5 


3 


'9 


4 














214 


210 


4 





1 


1 







4 


'9 


i2 


'9 


i9 


2 


'6 


223 


236 


5 


19 





1 


3 


*2 


9 


17 


17 


19 


18 





9 


206 


226 


6 


2 


2 


2 


1 


6 


12 


26 


18 


15 


20 


19 


27 


231 


239 


7 





6 


6 


3 


6 


1 


22 


18 


14 


15 


15 


22 


217 


209 


8 


6 


20 


5 


4 


4 


10 


23 


31 


20 


20 


13 


6 


224 


235 


9 


14 


8 


7 


2 


13 


9 


31 


18 


16 


20 


25 


29 


213 


235 


10 





2 











2 


27 


18 


12 


19 


1 


2 


235 


244 


11 


6 


10 


2 


2 


6 


5 


20 


14 


16 










217 


219 


12 


9 


4 


4 


1 


12 




















13 


19 


16 


5 


2 


5 


i9 


27 


is 


i7 


17 


'8 


20 


2ii 


207 


14 


27 


25 


3 


3 


2 


4 


21 


45 


15 


12 


1 


1 


2*>1 


233 


15 


9 


2 


7 


6 





2 


37 


22 


12 


17 


4 


6 


230 


219 


16 






5 


1 


3 


15 


32 


30 


18 


20 


4 


1 


205 


201 


17 


i9 


i<5 


5 


6 


1 


1 


38 


23 


14 


13 


7 


6 


235 


229 


18 


9 


10 





2 


5 


9 


28 


9 


18 


14 








220 


234 


19 


16 


3 





1 


9 


6 


29 


18 


19 


8 


2 


12 


213 


230 


20 


4 


17 


1 


2 


1 


4 


27 


27 


20 


20 


11 


11 


210 


214 


21 


6 


3 


1 


2 





4 


18 


17 


12 


10 








205 


197 


22 


9 


25 





o 


15 


22 


37 


23 


IS 


20 


27 


29 


204 


216 


23 


11 


19 


4 


o 


14 


20 




37 




20 


5 


2 


231 


233 


24 


16 


7 


3 


3 


8 


12 


22 


34 


15 


. 18 


22 


30 


231 


231 


25 


9 





3 


1 


6 


13 


23 


17 


18 


8 


9 


13 


241 


231 


26 


23 


5 


6 


6 


15 


24 


28 


23 


20 


20 


26 


18 


198 


219 


27 


16 





1 


3 


6 


4 


22 


13 


18 


17 


2 


7 


214 


207 


28 


8 


4 


2 


2 


10 


18 


25 


23 


15 


14 


15 


25 


230 


216 


29 


18 


6 


6 


3 


4 


4 


2° 


18 


12 


9 


8 


4 


207 


206 


30 


16 


6 


4 


4 


6 


10 


25 


22 


20 


20 


9 


12 


223 


236 


31 


10 


12 


2 


3 


1 


6 


26 


23 


20 


17 




5 


232 


226 


32 








2 


1 








21 


14 


17 


5 






?'^8 


238 


33 


2 


4 






3 


6 


24 


11 




14 


8 


15 


247 


227 


34 


3 


8 


2 


i 




3 


12 


23 


20 


19 


9 


6 


230 


244 


35 


9 


10 


4 


3 


'(3 


6 


19 


9 


9 


11 


1 


9 


195 


219 


36 


17 


4 


2 


3 


14 


28 


35 


19 


18 


19 


11 


10 


203 


212 


37 












10 


21 


13 


18 






29 


215 


216 


38 


27 


5 


i 


'4 


7 


10 


24 


23 


20 


ij> 


5 


21 


209 


227 


39 


6 


o 


1 


3 


7 


10 


18 


15 


11 


19 


8 


11 


236 


237 


40 





8 


1 


1 


2 


3 


25 


18 


10 


9 


14 


19 


211 


216 


41 


16 


1 


2 


2 


2 


5 


5 


16 










210 


215 


42 


8 


4 


2 


2 


6 


9 






15 


20 




2 


202 


226 


43 


17 


4 


4 


2 


6 


15 


17 


24 


13 


20 


14 


20 


217 


226 


44 


26 


24 


10 


6 


11 


18 


16 


8 


20 








218 


210 


45 


11 


4 


2 


3 


5 


18 


22 


18 


16 


i9 


20 


29 


226 


226 


46 


8 


7 


o 


2 


16 








20 


20 


21 


27 


208 


214 



498 353 137 117 250 416 970 839 658 647 346 510 9803 10010 



Individual and Composite Scores 67 



TABLE 41— GIRLS' SCORES 



Girl 


Bl 


B2 


B3 


B4 


B5 


B6 


CI 


C2 


C3 


C4 


C5 


C6 


C7 


C8 


1 


10 


24 


2 


2 


14 


10 


3 


3 


32 


31 


32 


31 


31 


31 


2 


5 


11 


2 


4 


16 


13 


3 


5 


33 


33 


33 


32 


31 


33 


3 


3 


4 


2 


2 


10 


14 


4 


4 


33 


33 


31 


30 


34 


29 


4 


8 


9 


2 


4 


14 


14 


1 


5 


32 


31 


34 


28 


34 


30 


5 





4 





2 


11 


15 


3 


2 


34 


31 


32 


32 


31 


27 


6 


3 


6 


2 


1 


13 


16 


2 


2 


33 


33 


32 


29 





28 


7 


2 


4 





4 


14 


14 


1 


2 


32 


36 


22 


25 


27 


29 


8 


4 


4 


2 


2 


14 


12 


5 


4 


30 


34 


33 


31 


26 


31 


9 


4 


19 


4 


4 


14 


14 


3 


2 


33 


31 


— 


30 


27 


29 


10 


4 


11 


2 





14 


2 


3 


2 


36 


34 


33 


27 


30 


31 


11 


4 





2 


2 


11 





2 


2 


33 


28 


30 


29 


33 


28 


12 


2 


4 


1 


4 








— 


— 


36 


29 


31 


— 


28 


30 


13 


4 





2 


4 


15 


15 


3 


3 


34 


35 


31 


31 


33 


33 


14 


2 


10 


2 


2 


10 


13 


3 


3 


25 


28 


34 


32 


31 


30 


15 


4 


4 


4 


4 


16 


11 


2 


2 


30 


33 


29 


— 


28 


27 


16 


6 


16 





4 


_ 


14 





4 


31 


33 


32 


34 


29 


26 


17 


4 


7 


2 


4 


10 


11 


3 


3 


30 


31 


29 


29 


28 


25 


18 


1 


4 


2 


2 


14 


15 


1 


2 


30 


29 


32 


28 


25 


31 


19 


16 


28 


2 


6 


16 


12 


2 


2 


25 


31 


29 


29 


29 


29 


20 


3 


2 


2 





15 


14 


2 


3 


37 


37 


34 


35 


28 


33 


21 


8 


4 


2 


2 


8 


14 


2 


3 


35 


29 


32 


28 


32 


28 


22 


16 


10 





3 


10 


16 


4 


3 


32 


32 


31 


33 


34 


32 


23 


9 


13 





4 


16 


12 


4 


3 


37 


— 


30 


34 


33 


33 


24 


18 


36 


3 





12 


12 


3 


2 


34 


32 


35 


34 


34 


34 


25 


2 


2 


2 





14 


14 


5 


3 


34 


34 


29 


30 


29 


27 


26 














14 





1 


2 


31 


30 


31 


31 


27 


27 


27 


4 


3 


3 


2 


11 


13 


1 


2 


32 


36 


30 


29 


26 


30 


28 


13 





4 


4 


12 


15 


4 


3 


— 


35 


— 


26 


— 


29 


29 


7 





2 


2 


13 





1 





31 


32 


29 


24 


27 


20 


30 


8 


5 


3 


4 


13 





1 


3 


34 


35 


33 


33 


34 


31 


31 


5 


12 


1 


3 


16 


13 


4 


3 


29 


32 


31 


31 


31 


30 


32 


2 





3 


1 


15 


13 


— 


— 


30 


33 


29 


31 


31 


27 


33 


7 


12 


2 


4 








1 


1 


33 


— 


28 


21 


29 


24 


34 


8 


4 


4 


2 


14 


11 


4 


3 


35 


34 


32 


34 


30 


33 


35 


6 


22 


2 


2 


12 


11 


2 


2 


27 


35 


— 


21 


29 


30 


36 


1 


6 


2 


2 





12 








30 





25 





26 





37 


— 


— 


— 


— 


16 


15 


3 


3 


30 


33 


33 


31 


29 


33 


38 


10 


6 


2 





16 


14 


3 


3 


26 


23 


31 


23 


28 


29 


39 


14 





3 


2 


12 


13 


3 





29 


32 


30 


24 


23 


24 


40 


10 


4 


1 


2 


16 


11 


2 


2 


33 


30 


28 


32 


31 


33 


41 


2 


7 





4 





12 








29 


33 


27 


26 


31 


30 


42 


2 


5 





4 


13 


12 


3 


3 


32 


33 


29 


28 


33 


30 


43 


4 


4 


1 


2 


9 


13 


4 


3 


34 


36 


35 


29 


30 


32 


44 


1 


6 


3 


4 


15 


14 


3 


5 


35 


37 


27 


30 


33 


34 


45 


8 


12 


1 


4 


12 





3 


5 


36 


36 


33 


32 


34 


32 


46 


6 


5 


4 


4 


14 


13 


— 


— 


35 


29 


33 


34 


34 


32 




260 


349 


87 


120 


544 


502 


107 


114 


1442 


1392 


1324 


1271 


1321 


1334 



68 The Interrelations of Mental Abilities 



TABLE 41— GIRLS' SCORES 
Girl Dl D2 D3 D4 D5 D6 El E2 E3 E4 E5 E6 E7 E8 



1 


2 


4 


5 


4 


4 


4 


10 


11 


21 


12 


23 


26 


16 


16 


2 


5 


4 


6 


3 


5 


5 


12 


3 


23 


18 


35 


39 


34 


36 


3 


5 


5 


— 


— 


3 


3 


12 


7 


. — 


— 


32 


27 


34 


35 


4 


5 


3 


3 


4 


4 


4 


12 


6 


20 


9 


15 


21 


15 


16 


5 


2 


1 


1 


3 





4 


10 


8 


9 


11 


16 


17 


20 


20 


6 


4 


3 


5 


4 


3 


4 


11 


8 


20 


14 


23 


20 


20 


16 


7 


2 


1 


3 


2 





3 


8 


9 


25 


14 


24 


19 


16 


13 


8 


5 


5 


6 


5 


4 


5 


10 


8 


18 


— 


40 


40 


36 


37 


9 


4 


3 


4 


4 


2 


2 


10 


10 


25 


13 


32 


28 


36 


.36 


10 


3 


4 


4 


2 


4 


4 


12 


7 


15 


9 


21 


24 


14 


28 


11 


3 


1 


3 


4 


4 


3 


10 


9 


. . 


6 


22 


22 


19 


30 


12 


— 


— 


— 


— 


4 


3 


— 


— 


. — 


— 


28 


25 


28 





13 


3 


3 


4 


3 


2 


4 


10 


6 


11 


7 


25 


25 


22 


25 


14 


3 


3 


4 


3 


2 


4 


9 


9 


26 


10 


21 


19 


12 


19 


15 


2 


9 


3 


4 


3 


2 


6 


6 


19 


10 


— 


— 


17 


21 


16 


5 


4 


4 


3 


4 


5 


11 


9 


18 


13 


25 


25 


29 


26 


17 


o 


2 


3 


1 


3 


5 


— - 


6 


20 


20 


— 


26 


19 


13 


18 


2 





2 


2 


3 


4 


10 


9 


21 


15 


16 


19 


12 


24 


19 


4 


3 


2 


4 


2 


4 


11 


8 


18 


11 


33 


28 


25 


28 


20 


3 


4 


4 


5 


3 


5 


7 


8 


11 


5 


21 


21 


13 


18 


21 


2 


4 


5 


5 


4 


4 


10 


9 


20 


17 


31 


27 


20 


19 


22 


3 


5 


5 


3 


2 


3 


11 


10 


19 


9 


28 


25 


29 


32 


23 


4 


3 


5 


6 


4 


5 


8 


11 


12 


— 


28 


33 


35 


36 


24 


2 


2 


4 


4 


4 


3 


10 


8 


19 


15 


18 


12 


8 


18 


25 


1 


o 


3 


3 


O 


3 


11 


11 


18 


2 


33 


27 


26 


18 


26 








3 


5 


3 


3 


10 


6 


21 


8 


25 


20 


17 


24 


27 


4 


2 


5 


4 


2 


2 


10 


8 


22 


6 


24 


20 


16 


11 


28 


4 


4 


4 


4 


3 


3 


12 


10 


22 


6 


38 


36 


— 


31 


29 


] 





2 


2 


2 


4 


10 


4 


13 


6 


13 


15 


13 


17 


30 


4 


1 


4 


5 


1 


3 


12 


9 


22 


13 


26 


31 


20 


27 


31 


2 


3 


4 


5 


1 


3 


10 


10 


18 


9 


35 


31 


13 





32 


— 


. — 


6 


4 


2 


4 


7 


10 


13 


— 


18 


12 


15 


1 


33 








1 


1 





2 


9 


8 


— 


6 


— 


— 


14 


13 


34 


5 


3 


6 


4 


4 


5 


11 


9 


IS 


12 


32 


29 


28 


34 


35 


4 


2 


3 


o 


3 


5 


9 


10 


18 


8 


26 


28 


31 


33 


36 








4 


3 


5 


3 





10 


14 


9 


20 


11 


14 


10 


37 


4 


3 


5 


4 


5 


5 


5 


8 


16 


10 


31 


28 


33 


34 


38 


1 


3 


3 


2 





•-> 


12 


5 


20 


12 


— 


— 


6 


9 


39 


1 


1 


2 


3 


2 


3 


11 


6 


13 


10 


23 


22 


12 


12 


40 


2 


4 


4 


4 


4 


4 


11 


8 


23 


7 


20 


22 


16 


13 


41 














3 


3 





8 








28 


25 


10 


19 


42 


4 


3 


2 


5 


5 


4 


11 


10 


18 


13 


— 


— 


21 


19 


43 


5 


3 


5 


3 


5 


2 


12 


4 


28 


13 


28 


27 


31 


34 


44 


4 


3 


6 


6 


4 


5 


12 


10 


22 


. — 


44 


38 


38 


37 


45 


3 


4 


5 


3 


4 


4 


10 


8 


24 


14 


38 


32 


35 


33 


46 


— 


— 


5 


3 


5 


5 


11 


11 


10 


6 


25 


26 


32 


39 



124 110 167 153 138 169 426 368 763 408 1084 1048 970 1030 



Individual and Composite Scores 69 



TABLE 41— GIRLS* SCORES 
Girl E9 E10 Ell E12 E13 E14 E15 E16 E17 E18 Fl F2 F3 F4 



1 


28 


25 


10 


12 


26 


31 


83 


77 


101 


48 





2 


1 


2 


2 


27 


32 


13 


14 


31 


33 


86 


78 


92 


51 


1 


1 


4 


3 


3 


26 


32 


13 


14 


27 


29 


93 


65 


70 


48 


2 


— 


1 


3 


4 


27 


34 


9 


13 


25 


26 


78 


71 


88 


47 


2 


2 


3 


3 


5 


22 


30 


6 


10 


29 


29 


78 


75 


88 


46 


1 





2 





6 


27 


28 


9 


12 


20 


27 


72 


66 


64 


49 





2 





2 


7 


30 


22 


9 


12 


25 


31 


74 


71 


87 


46 





3 


5 


2 


8 


32 


40 


12 


13 


37 


36 


94 


78 


112 


46 


2 


2 


4 


3 


9 


26 


32 


14 


12 


24 


28 


82 


68 


99 


48 





4 


3 


3 


10 


29 


29 


10 


10 


20 


28 


80 


67 


89 


46 


1 


2 


3 


3 


11 


20 


30 


11 


11 


27 


29 


75 


63 


96 


46 








2 


2 


12 


23 


36 


— 


— 


22 


27 


79 


70 




44 


— 


— 


— 


— 


13 


26 


28 


15 


12 


25 


26 


74 


61 


80 


51 


1 


1 


3 


1 


14 


20 


22 


11 


10 


27 


30 


57 


67 


89 


44 


1 





2 


1 


15 


26 


28 


9 


9 


26 


30 


74 


64 


89 


42 


2 


2 


4 


3 


16 


30 


28 


11 


12 


28 


26 


78 


67 


99 


49 





1 


3 


5 


17 


28 


33 


7 


9 


20 


24 


69 


65 


71 


42 


1 


2 


2 


3 


18 


24 


25 


6 


9 


24 


20 


70 


62 


73 


45 


4 


1 


3 


2 


19 


26 


26 


15 


14 


28 


32 


78 


70 


97 


49 


1 


2 


3 


5 


20 


28 


37 


12 


13 


24 


26 


71 


65 


92 


49 


2 


2 


3 


3 


21 


29 


39 


14 


9 


28 


29 


78 


69 


96 


47 


3 


2 


2 


3 


22 


27 


44 


10 


12 


31 


34 


92 


74 


105 


47 


2 


1 


4 


2 


23 


27 


40 


12 


14 


27 


30 


84 


69 


79 


— 


4 


3 


3 


2 


24 


26 


32 


8 


14 


23 


27 


60 


63 


71 


47 








4 


3 


25 


23 


28 


11 


11 


35 


39 


98 


79 


99 


48 


2 





5 


3 


26 


28 


21 


12 


13 


28 


23 


64 


62 


86 


45 


1 








3 


27 


22 


24 


9 


11 


21 


25 


73 


68 


85 


47 


2 


1 





2 


28 


28 


34 


9 


11 


27 


33 


98 


77 


113 


48 


2 


4 


4 


5 


29 


28 


20 


6 


5 


22 


18 


53 


56 


93 


48 











3 


30 


28 


29 


8 


7 


29 


29 


79 


67 


99 


46 


2 


1 


2 


5 


31 


30 


40 


15 


13 


24 


29 


88 


78 


95 


44 


3 


1 





3 


32 


22 


29 


— 


— 


24 


27 


61 


60 


75 


— 


2 


2 


1 


3 


33 


19 


23 


14 


10 


20 


18 


72 


67 


72 


44 














34 


32 


32 


13 


14 


25 


34 


75 


68 


80 


47 


2 


1 





3 


35 


28 


26 


9 


9 


29 


35 


81 


72 


95 


51 


2 


2 





3 


36 


24 


28 





10 


19 


25 


74 


64 


76 


44 











3 


37 


32 


27 


8 


13 


19 


27 


— 


70 


90 


45 


2 


1 


2 


2 


38 


24 


20 


9 


12 


26 


22 


76 


67 


82 


44 


2 


1 


2 


3 


39 


18 


30 


8 


12 


23 


25 


65 


62 


77 


37 





2 


2 


2 


40 


14 


24 


9 


11 


19 


26 


78 


63 


87 


43 


2 


1 


3 


1 


41 


22 


36 








25 


28 


78 


73 


78 


48 











_ 


42 


26 


36 


13 


11 


18 


29 


95 


82 


112 


— 


3 


2 


4 


3 


43 


21 


30 


8 


— 


25 


27 


87 


69 


101 


48 


1 


2 





2 


44 


32 


46 


14 


— 


35 


36 


98 


92 


116 


50 


4 


2 


6 


3 


45 


32 


32 


11 


13 


24 


26 


94 


71 


106 


48 











3 


46 


26 


38 


— 


13 


33 


30 


76 


73 


93 


51 


2 


2 


3 


5 




1193 


1405 


432 


469 


1174 


1299 


3522 


3185 


4037 


2003 


64 


60 


98 


119 



70 The Interrelations of Mental Abilities 



TABLE 42— BOYS' DEVIATIONS OF THE COMPOSITES 



Boy 

1 
2 


#A1 


#A2 


#b: 


L #B2 


! #C1 


#C2 


#D1 


#D2 


#E1 


#E2 


#F1 


#F2 


69 


101 


2 


3 


—6 


10 


4 


—1 


—12 


—35 


—1 


— 1 


3 

4 
5 


53 


55 


10 


17 


3 


8 


3 





73 


58 


3 


2 


—113 


—126 


—l 


—12 


—2 


—1 


1 


2 


—10 


—21 


1 


2 


6 


126 


94 


23 


30 


4 


6 


—1 


—3 


—13 


—20 


—2 


1 


7 


—23 


26 


—9 


— 4 


—7 





2 


—2 


62 


36 


3 


2 


8 


—14 


—32 


—36 


7 


6 


—6 


2 





—SO 


—65 


—2 





9 


—37 


—25 


2 


—11 


10 


5 


2 


—2 


2 


—23 


—1 





10 


36 


2 


—14 


—3 


17 


14 


4 


2 


61 


63 


3 





11 


—91 


—16 


—4 


—11 


13 


8 


3 


4 


—3 


25 


1 


— 1 


12 


—144 


—138 


—14 


—6 


—25 


—16 


—1 


—^ 


—48 


—18 


3 


2 


13 


—37 


—45 


2 


—3 


2 


—1 


—2 


2 


37 


—20 





« 


14 


86 


101 


10 


18 


— 5 


—1 


—3 


—3 


—18 


9 


1 


1 


15 


—82 


—70 


—18 


—15 


—3 


—14 





2 


21 


2 


2 


2 


16 


53 


39 


—19 


8 


3 


—9 


1 


1 


15 


5 


2 


— 1 


17 


34 


50 


14 


4 


7 


—3 


—1 





—1 


5 


2 


1 


18 


























19 


—100 


—86 


1 


1 


o 





o 


—1 


—128 


—89 


—1 


2 


20 


























21 


—10 


—38 


o 


5 


—12 


—17 


2 


—1 


—71 


—34 








22 


32 


37 


16 


—10 


—3 


2 


— 5 


—1 


—34 


—59 


—2 





23 


90 


31 


—11 


9 


7 


—5 





—3 


22 


2 








24 


9 


6 


13 


19 


7 


11 


—1 


1 


11 


—45 


—1 


1 


25 


33 


9 


7 


12 


1 


—1 


2 


2 


4 


44 





—1 


26 


—12 


—11 


9 


—14 


7 


10 


1 


—1 


44 


46 


2 


1 


27 


16 


22 


12 


12 


— 5 


—3 


3 


2 


—51 


—28 


2 


2 


28 


























29 


—30 


—75 


—24 


—14 


5 


3 








—47 


—59 


—3 


—2 


30 


121 


72 


20 


20 


—12 


—6 


—4 


—4 


42 


47 


3 


2 


31 


—31 


—19 


14 


24 


14 


6 


4 


4 


27 


14 


—2 





32 


53 


55 


6 


5 


5 


7 


o 


2 


11 


10 


—1 


—1 


33 


—76 


—108 


—24 


—6 


—19 


—11 


—8 


—5 


3 


—35 


1 


1 


34 


18 


60 


8 


1 


8 


12 


2 


—1 


29 


9 


2 


1 


35 


























36 


4 


28 


8 


12 


6 


6 


1 


1 


52 


45 


3 


5 


37 


—120 


—43 

786 


—20 
194 


— 5 

207 


4 
129 


10 
116 


5 
40 


—1 
23 


1 

493 


17 
435 


2 

30 


1 




833 


36 




—920 


—864 


—179 


—114 


-101 


—99 


—32 


—35 


—540 


—553 


—22 


—7 



Individual and Composite Scores Jl 



TABLE 43— GIRLS' DEVIATIONS OF THE COMPOSITES 
Girl #A1 #A2 #B1 #B2 #C1 #C2 #D1 #D2 #E1 #E2 #F1 #F2 



1 


—24 


—51 


2 


14 


2 


1 


1 


1 


17 


2 


2 





2 
3 
4 


61 


71 


3 


13 


4 


10 


6 


1 


58 


61 


2 





—124 


—78 


8 


7 


3 


1 


2 





—12 


—12 


2 


1 


5 


—28 


—23 


—6 


—12 


4 


—4 


—7 


— 3 


—59 


—10 







6 


—4 


24 


7 


—10 


—2 


—4 


2 





—37 


—11 


—3 





7 


-A 


—19 


—6 


2 


—16 


—4 


—5 


— 5 


5 


—27 


2 


1 


8 


18 


56 





—6 





6 


5 


4 


92 


70 


3 


1 


9 


97 


37 


12 


17 


—2 


—4 





—2 


51 


33 





3 


10 


—84 


—66 


—20 


—7 


6 


—2 


1 


—1 


—17 


—16 


1 


1 


11 


-^2 


—53 


—24 


—16 


1 


—9 





—3 


—37 


—18 


—1 


—2 


12 


























13 


33 


53 


6 





5 


7 


—1 


—1 


—37 


—26 


1 


—2 


14 


—6 


28 





—8 


—3 


2 


—1 


—1 


—37 


—44 





—3 


15 


2 


—22 


6 


6 


—8 


—6 


—2 


—3 


—25 


—35 


3 


1 


16 


17 


17 


6 


18 


1 


3 


3 


1 


28 


4 





2 


17 


29 


—11 


—2 


—3 


—6 


—7 


—2 


—3 


—38 


—2 





1 


18 


—27 


—59 


3 


—6 


—10 


—6 


—3 


—5 


—53 


—29 


4 


—1 


19 


9 


—70 


12 


38 


—12 


—5 


2 





22 


5 


1 


3 


20 


—15 


22 


3 


—14 


4 


13 





3 


—48 


—9 


•» 


1 


21 


—86 


—88 


8 


—18 


4 


—7 


1 


2 


25 


42 


2 


1 


22 


75 


120 


12 


—4 


6 


5 








47 


60 


3 


—1 


23 


58 


76 


—3 


15 


9 


12 


3 


3 


—13 


41 


4 


1 


24 


34 


76 


18 


14 


10 


6 





—2 


—66 


—7 


1 


—1 


25 


2 


—55 


2 


—8 


3 


—1 


-A 


—3 


39 


—7 


4 


—1 


26 


127 


88 


22 


2 


—8 


—6 


—4 


—3 


—10 


—63 


—2 


—1 


27 


—12 


—54 


~6 


—13 


—9 


1 


1 


—3 


—29 


—57 


—1 


—1 


28 


10 


34 


23 


—6 





—2 


1 





81 


34 


3 


5 


29 


4 


—70 


—21 


—12 


—10 


—22 


—5 


—5 


—66 


—103 


—3 


—1 


30 


34 


22 


—16 


1 


4 


7 


—1 


—2 


28 


6 


1 


2 


31 


—17 


—8 


—1 


10 





1 


—3 





25 


16 








32 


























33 


























34 


—51 


—9 


10 


—6 


6 


9 


5 


1 


17 


32 


—1 





35 


—52 


—56 





8 


—17 


—8 





2 


17 


11 


—1 


1 


36 


























37 


























38 


31 


36 


10 


—8 


—8 


—17 


—6 


—4 


—26 


—66 


1 





39 


—53 


—12 


16 


—14 


—11 


—14 


—5 


—4 


—85 


—55 


—1 





40 


—58 


—51 





—2 


—3 


1 





1 


—46 


—62 


2 


—2 


41 


























42 


—61 


—11 


—10 


1 


1 


—1 


1 


1 


31 


37 


4 


1 


43 


2 


41 


—2 


—16 


8 


5 


5 


—3 


44 


2 


2 





44 


87 


66 


5 


6 


2 


13 


4 


3 


124 


127 


7 


1 


45 


9 


58 


—24 


6 


10 


12 


2 





87 


33 


—3 


—1 


46 




























739 


925 


178 


178 


93 


113 


43 


21 


838 


616 


53 


27 




-748 —866 - 


-157 - 


-189 - 


-125 - 


-131 


—51 


—58 - 


-741 - 


-659 


—20 


—21 



72 The Interrelations of Mental Abilities 



TABLE 44— ARITHMETIC AVERAGES 













Highest 




Boys 




Girls 




possible 












! 


Score 


Al & A2 


17.17 


15.61 


11.32 


8.02 


55 


55 


A3 & A4 


5.14 


4.14 


3.11 


2.66 


28 


27 


A5 & A6 


6.06 


8.69 


5.95 


9.45 


35 


35 


A7 & A8 


28.82 


16.S4 


23.66 


19.98 


56 


70 


A9 & A10 


15.47 


16.31 


16.05 


16.18 


20 


20 


All & A12 


14.19 


21.52 


9.35 


12.44 


30 


30 


A13 & A14 


208.64 


210.57 


217.84 


222.44 


288 


288 


Bl & B2 


9.57 


10.76 


5.91 


7.93 


48 


48 


B3 & B4 


3.05 


2.35 


1.98 


2.73 


10 


8 


B5 & B6 


11.86 


13.28 


12.95 


11.16 


16 


16 


CI & C2 


3.34 


3.43 


2.68 


2.78 


5 


5 


C3 & C4 


33.31 


31.95 


32.04 


32.37 


38 


38 


Co & C6 


29.71 


29.05 


30.79 


29.56 


35 


35 


C7 & C8 


28.41 


28.58 


30.02 


29.64 


36 


36 


Dl & D2 


3.66 


3.00 


3.02 


2.68 


5 


5 


D3 & D4 


4.36 


3.67 


3.88 


3.56 


6 


6 


Do & D6 


3.11 


4.08 


3.00 


3.67 


6 


6 


El & E2 


9.86 


8.14 


10.14 


8.18 


12 


12 


E3 & E4 


19.18 


11.90 


18.61 


10.46 


37 


20 


E5 & E6 


28.70 


25.92 


26.44 


24.95 


50 


50 


E7 & E8 


18.84 


23.32 


21.56 


22.89 


40 


40 


E9 & E10 


25.11 


32.30 


25.93 


30.54 






Ell & E12 


9.49 


11.24 


10.54 


11.44 


15 


15 


E13 & E14 


27.19 


29.86 


25.52 


28.24 


43 


43 


E15 & E16 


79.81 


72.58 


78.27 


69.24 


104 


100 


E17 & E18 


97.78 


47.03 


89.71 


46.58 


130 


54 


Fl & F2 


1.00 


1.38 


1.42 


1.43 


4 


4 


F3 & F4 


2.19 


2.56 


2.28 


2.70 


5 


7 



Individual and Composite Scores 



76 



TABLE 45 
RELIABILITY COEFFICIENTS : 



TABLE 46 
RELIABILITY COEFFICIENTS : 



Paired 


Tests arrani 


?ed 


according to 


Paired 


Tests arranged accordin 


e to 








tne uroups 






Magnitude of 


the Coefficient 








Boys 


Girls 
























n 


r 


n 


r 


Boys 




Girls 






Al 


& 


A2 


36 


61 


44 


37 








r 








r 


A3 


& 


A4 


37 


62 


44 


56 


All 


& 


A12 


76 


E5 


& 


E6 


87 


A5 


& 


A6 


35 


58 


40 


72 


A9 


& 


A10 


69 


All 


& 


A12 


84 


A7 


& 


A8 


34 


41 


41 


24 


A13 


& 


A14 


68 


E7 


& 


E8 


82 


A9 


& 


A10 


31 


69 


38 


34 


Bl 


& 


B2 


67 


E15 


& 


E16 


77 


All 


& 


A12 


29 


76 


37 


84 


E15 


& 


E16 


66 


A5 


& 


A6 


72 


A13 


& 


A14 


37 


68 


45 


59 


E7 


& 


E8 


65 


E13 


& 


E14 


65 
















E5 


& 


E6 


65 


A13 


& 


A14 


59 


Bl 


& 


B2 


37 


67 


44 


48 


A3 


& 


A4 


62 


A3 


& 


A4 


56 


B3 


& 


B4 


37 


51 


44 


—07 


E13 


& 


E14 


62 


Dl 


& 


D2 


55 


B5 


& 


B6 


32 - 


-18 


42 


27 


Al 


& 


A2 


61 


Bl 


& 


B2 


48 


CI 


& 


C2 


35 


41 


40 


46 


Ell 


& 


E12 


61 


C5 


& 


C6 


48 


C3 


& 


C4 


36 


29 


42 


38 


A5 


& 


A6 


58 


CI 


& 


C2 


46 


C5 


& 


C6 


35 


50 


40 


48 


B3 


& 


B4 


51 


C7 


& 


C8 


49 


C7 


& 


C8 


33 


34 


43 


45 


C5 


& C6 


50 


D3 


& 


D4 


44 
















CI 


& 


C2 


41 


Ell 


Sc 


E12 


43 


Dl 


& 


D2 


35 


20 


41 


55 


















D3 


& 


D4 


33 


16 


43 


44 


A7 


& 


A8 


41 


D5 


& 


D6 


42 


D5 


& 


D6 


37 


27 


46 


42 


E9 


& 


E10 


40 


E3 


& 


E4 


41 
















C7 


& 


C8 


34 


C3 


& 


C4 


38 


El 


& 


E2 


36 


31 


42 


—15 


El 


& 


E2 


31 


Al 


<fc 


A2 


37 


E3 


& 


E4 


30 


21 


37 


41 


Fl 


& 


F2 


30 


A9 


& 


A10 


34 


E5 


& 


E6 


37 


65 


41 


86 


















E7 


& 


E8 


37 


65 


44 


82 


C3 


& 


C4 


29 


E9 


& 


E10 


34 


E9 


& 


E10 


37 


40 


46 


34 


D5 


& 


D6 


27 


Fl 


& 


F2 


32 


Ell 


& 


E12 


33 


61 


39 


43 


E3 


& 


E4 


21 


B5 


& 


B6 


27 


E13 


& 


E14 


37 


62 


46 


65 


Dl 


& 


D2 


20 


E17 


& 


E18 


26 


E15 


& 


E16 


36 


66 


45 


77 


F3 


& 


F4 


19 


A7 


Sc 


A8 


24 


E17 


& 


E18 


34 


05 


42 


26 
































D3 


& 


D4 


16 


F3 


& 


F4 


14 


Fl 


& 


F2 


32 


30 


42 


32 


E17 


& 


E18 


05 


B3 


& 


B4 


—07 


F3 


& 


F4 


30 


19 


43 


14 


B5 


& B6 


—18 


El 


& E2 


—15 








TABLE 


47 












TABLE 48 









Reliability Coefficients of the Com- 
posites arranged according to 
the Groups 

Boys Girls 

31 90 38 77 



Reliability Coefficients of the Com- 
posites arranged according to the 
Magnitude of the Coefficients 



#A1 & #A2 
#B1 & #B2 
#C1 & #C2 
#D1 & #D2 

#E1 & #E2 
#F1 & #F2 



31 
31 
31 
31 
31 



55 
70 
56 
82 
39 



38 
38 
38 
38 
38 



17 
69 
70 
80 
24 



Boys 

#A1 & #A2 
#E1 & #E2 
#C1 & #C2 
#D1 & #D2 
#B1 & #B2 
#F1 & #F2 



90 
82 
70 
56 
55 
39 



Girls 

#E1 & #E2 
#A1 & #A2 
#D1 & #D2 
#C1 & #C2 
#F1 & #F2 
#B1 & #B2 



80 
77 
70 
69 
25 
17 



TABLE 49 
RAW CORRELATIONS OF THE MANIPULATIVE TESTS 



Boys Al A2 

Al 61 

A2 61 

A3 27 37 

A4 25 13 

A5 42 36 

A6 26 25 

A7 41 45 

AS 16 23 

A9 52 28 

A10 36 10 

All 31 17 

A12 19 09 

A13 —35 —10 

A14 —39 —22 



A3 

27 
37 

62 
09 
15 
30 
33 
33 
16 
26 
05 



A4 
25 
13 
62 

17 
38 
44 
18 
34 
15 
48 
26 



-08 —22 
-08 —29 



A5 
42 
36 
09 
17 

58 
24 
30 
39 
35 
44 
20 
—25 
—33 



A6 
26 
25 
15 

38 

58 

31 

27 
49 
38 
68 
54 
—24 



A7 
41 
45 
30 
44 
24 
31 

41 
46 
15 
22 
23 
-13 



—17 —18 



A8 
16 
23 
33 
18 
30 
27 
41 

40 
05 
15 

—01 
07 

—05 



A9 A10 

52 



28 
33 
34 
39 
49 
46 
40 



53 



10 
16 
15 
35 
38 
15 
05 



51 

22 21 

—02 37 

—11 21 



All 
31 
17 
26 
48 
44 
68 
22 
15 
53 
51 

76 
—17 

—22 



A12 
19 
09 
05 
26 
20 
54 
23 

—01 
22 
21 
76 

—13 

03 



A13 A14 

—35 —39 

—10 —22 

—08 —08 

22 —29 

—25 —33 

—24 —17 

—13 —18 

07 —05 

—02 —11 

37 21 

—17 —22 

—13 03 

68 

68 



74 The Interrelations of Mental Abilities 















TABLE 


50 
















RAW 


CORRELATIONS OF 


THE MANIPULATIVE 


TESTS 




Girls 


Al 


A2 


A3 


A4 


A5 


A6 


A7 


A8 


A9 


A10 


All 


A12 


A13 


A14 


Al 




37 


34 


51 


29 


39 


09 


22 


36 


11 


—01 


08 


—29 


—24 


A2 


37 




27 


28 


16 


23 


22 


41 


26 


18 


11 


—03 


—08 


—14 


A3 


34 


27 




56 


14 


12 


12 


08 


—03 


—02 


17 


02 


—12 


—28 


A4 


51 


28 


56 




04 


10 


18 


09 


19 


07 


05 


—04 


—11 


—15 


A5 


29 


16 


14 


04 




72 


22 


05 


37 


36 


58 


53 


—16 


—10 


A6 


39 


23 


12 


10 


72 




25 


15 


37 


42 


50 


40 


—16 


—15 


A7 


09 


22 


12 


18 


22 


25 




24 


16 


08 


26 


14 


—03 


—10 


A8 


22 


41 


08 


09 


05 


15 


24 




17 


27 


18 


—05 


08 


14 


A9 


36 


26 


—03 


19 


37 


37 


16 


17 




34 


26 


20 


01 


02 


A10 


11 


18 


—02 


07 


36 


42 


08 


27 


34 




41 


26 


03 


14 


All 


—01 


11 


17 


05 


58 


50 


26 


18 


26 


41 




84 


02 


04 


A12 


08 


—03 


02 


—04 


53 


40 


14 


—05 


20 


26 


84 




05 


—02 


A13 


—29 


—08 


—12 


—11 


—16 


—16 


-03 


08 


01 


03 


02 


05 




56 


A14 


—24 


—14 


—28 


—15 


—10 


—15 


-10 


14 


02 


14 


04 


—02 


56 





TABLE 51 
RAW CORRELATIONS OF THE SPATIAL RELATIONS TESTS 



Boys 


Bl 


B2 


B3 


B4 


B5 


B6 


Girls Bl 


B2 


B3 B4 


B5 


B6 


Bl 




67 


16 


33 


13 


13 




48 


15 04 


—07 


—03 


B2 


67 




12 


22 


30 


—09 


48 




00 09 


—02 


02 


B3 


16 


12 




51 


30 


—10 


15 


00 


—07 


—03 


08 


B4 


33 


22 


51 




28 


08 


04 


09 


—07 


—04 


02 


B5 


13 


30 


30 


28 




—18 


—07 


—02 


—03 —04 




27 


B6 


13 


—09 


—10 


08 


—18 




—03 


02 


08 02 


07 





TABLE 52 
RAW CORRELATIONS OF THE COMPUTATIONAL ARITHMETIC 
Boys CI C2 C3 C4 C5 C6 C7 C8 
CI 41 13 21 —03 31 14 24 



C2 


41 




23 


08 


13 


27 


11 


11 


C3 


13 


23 




29 


64 


55 


54 


43 


C4 


21 


08 


29 




38 


50 


23 


44 


C5 - 


-03 


13 


64 


38 




50 


47 


37 


C6 


31 


27 


55 


50 


50 




43 


47 


C7 


14 


11 


54 


23 


47 


43 




34 


C8 


24 


11 


43 


44 


37 


47 


34 




Girls 


















CI 




46 


10 


06 


23 


29 


19 


31 


C2 


46 




18 


24 


30 


38 


45 


52 


C3 


10 


18 




38 


20 


42 


38 


38 


C4 


06 


24 


38 




-10 


10 


05 


22 


C5 


23 


30 


20 - 


-10 




48 


28 


35 


C6 


29 


38 


42 


10 


48 




41 


54 


C7 


19 


45 


38 


05 


28 


41 




45 



C8 31 52 38 22 35 54 45 

TABLE 53 
RAW CORRELATIONS OF THE ARITHMETIC PROBLEMS 



Boys Dl 


D2 


D3 


D4 


D5 


D6 


Girls 


Dl 


D2 


D3 


D4 


D5 


D6 


Dl 


20 


25 


38 


31 


—04 






55 


57 


33 


51 


34 


D2 20 




40 


05 


32 


16 




55 




69 


37 


45 


34 


D3 25 


40 




16 


45 


oo 




57 


fin 




44 


49 


34 


D4 38 


05 


16 




35 


19 




33 


37 


44 




29 


23 


D5 31 


32 


45 


35 




27 




51 


45 


49 


29 




42 


D6 —04 


16 


22 


19 


27 






34 


34 


34 


23 


42 





TABLE 56 
RAW CORRELATIONS OF THE LOGICAL TESTS 



Boys Fl 


F2 


F3 


F4 


Girls Fl 


F2 


F3 


F4 


Fl 


30 


21 


36 




32 


30 


02 


F2 30 




24 


38 


32 




35 


18 


F3 21 


24 




19 


30 


35 




14 


F4 36 


38 


19 




02 


18 


14 





Individual and Composite Scores 



75 



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7 6 



The Interrelations of Mental Abilities 



TABLE 57 

CORRELATIONS OF THE PAIRED TESTS CORRECTED BY THE 
FORMULA FOR ATTENUATION 



BOYS 
Al-2 A3-4 A5-6 A7-8 A9-10 All-12 



GIRLS 
Al-2 A3-4 A5-6 A7-8 A9-10 All-12 



At & 2 


39 


53 


57 


42 


25 






75 


48 


69 


58 


06 


A3 & 4 


39 


29 


59 


35 


29 




75 




14 


30 


12 


07 


A5 & 6 


53 29 




57 


63 


63 




48 


14 




34 


76 


64 


A7 & 8 


57 59 


57 




37 


25 




69 


30 


34 




55 


25 


A9 &10 


42 35 


63 


37 




47 




58 


12 


76 


55 




51 


A11&12 


25 29 


63 


25 


47 


TABLE 


58 


06 


07 


64 


25 


51 




BOYS 












GIRLS 












Bl-2 B3-4 


B5-6 










Bl-2 B3-4 B5-6 








Bl & 2 


33 


49 












35 —07 








B3 & 4 


33 


84 










35 




10 








B5 & 6 


49 84 








TABLE 


59 


—07 


10 












BOYS 












GIRLS 












Cl-2 C3-4 C5-6 


C7-8 






Cl-2 


C3-4 C5-6 


C7-8 






CI & 2 


42 


38 


37 










31 


64 


75 






C3 & 4 


42 


132 


124 








31 




36 


47 






C5 & 6 


38 132 




105 








64 


36 




83 






C7 & 8 


37 124 


105 






TABLE 


60 


75 


47 


83 










BOYS 












GIRLS 












Dl-2 D3-4 


D5-6 










Dl-2 


D3-4 


D5-6 








Dl & 2 


112 


81 












95 


85 








D3 & 4 


112 


137 










95 




76 








D5 & 6 


81 137 








TABLE 


61 


85 


76 










Boys 


E1&2 


E3&4 


E5&6 


E7&8 E9&10 


E11&12 E13&14 


E15&16 


E17A18 


El & 2 




—34 




70 


59 


100 


72 




27 


52 




21 


E3 & 4 


—34 






20 


13 


-32 


—14 




12 


26 




160 


E5 & 6 


70 


20 






74 


93 


55 




76 


92 




66 


E7 & 8 


59 


13 




74 




56 


31 




52 


67 




21 


E9 &10 


100 


—32 




93 


56 




48 




51 


91 




63 


E11&12 


72 


—14 




55 


31 


48 






42 


45 




34 


E13&14 


27 


12 




76 


52 


51 


42 






78 




64 


E15&16 


52 


26 




92 


67 


91 


45 




78 






57 


E17&18 


21 


160 




66 


21 


63 


34 




64 


57 






Girls 


























El & 2 




14 




50 


37 


139 


74 




97 


108 




364 


E3 & 4 


14 






35 


17 


17 


00 


—03 


17 




—01 


E5 & 6 


50 


35 






77 


88 


73 




74 


88 




84 


E7 & 8 


37 


17 




77 




75 


48 




65 


5T 




96 


E9 &10 


139 


17 




88 


75 




66 




71 


82 




105 


E11&12 


74 


00 




73 


48 


66 






49 


52 




53 


E13&14 


97 


—03 




74 


65 


71 


49 






75 




106 


E15&16 


108 


17 




88 


57 


82 


52 




75 






103 


E17&18 


364 


—01 

Boys 
F3&4 




84 


96 
TABLE 


105 
62 


53 




106 

Girls 
F3&4 


103 






Fl & 2 




120 














61 









Individual and Composite Scores 



77 



TABLE 63— BOYS 

RAW CORRELATIONS OF THE COMPOSITES 

Non-Verbal 
Non- Verbal Computa- Verbal Very- 
Manipulative Spatial tion Arithmetic Verbal Logical 

(1) (2) (1) (2) (1) (2) (1) (2) (1) (2) (1) (2) 

Manipulative (1) 90 55 65 18 18—05—08 25 27 03—19 

(2) 90 . . 60 61 24 36 11 02 33 34 01 —13 

Non-Verbal Spatial(l) 55 60 .. 55 12 20—05 09 23 24 07 09 

(2) 65 61 55 .. 07 09 04 02 08 17 07 07 

Non-Verbal Computa- 
tion (1) 18 24 12 07 . . 70 60 61 29 26 —33 —22 

(2) 18 36 20 09 70 . . 53 31 40 29 —33 —09 

Verbal Arithmetic (1) .—05 11 —05 04 60 53 .. 56 17 33 —11 —25 

(2) .—08 02 09 02 61 31 56 . . 18 18 —07 —09 

Very-Verbal (1) 25 33 23 08 29 40 17 18 .. 82 38 26 

(2) 27 34 24 17 26 29 33 18 82 .. 51 12 

Logical (1) 03 01 07 07 —33 —33 —11 —07 38 51 . . 39 

(2) —19—13 09 07—22—09—25—09 26 12 39 .. 

TABLE 64— GIRLS 

Manipulative (1) 77 03 32 04 22 01 00 31 22 09 09 

(2) 77 .. 12 14 39 51 28 26 33 39 12 00 

Non-Verbal Spatial (1) 03 12 . . 17 —04 08 13 18 05 20 30 32 

(2) 32 14 17 .. —04 26 16 26 30 29 13 39 

Non-Verbal Computa- 
tion (1) 04 39—04—04 .. 69 52 52 28 48 12—11 

(2) 22 51 08 26 69 .. 68 67 47 63 32 05 

Verbal Arithmetic (1). 01 28 13 16 52 68 .. 70 55 64 12 28 

(2). 00 26 18 26 52 67 70 .. 50 68 34 28 

Very-Verbal (1) 31 33 05 30 28 47 55 50 .. 80 31 48 

(2) 22 39 20 29 48 63 64 68 80 .. 48 39 

Logical (1) 09 12 30 13 12 32 12 34 31 48 .. 25 

(2) 09 00 32 39 —11 05 28 28 48 39 25 

TABLE 65— CORRELATIONS OF THE COMPOSITES CORRECTED BY 
THE FORMULA FOR ATTENUATION 



Boys #A #B #C #D #E #F Girls #A #B #C #D #E #F 



#A 




86 


29 


01 


34 


—11 




30 


29 


19 


39 


10 


#B 


86 




18 


05 


25 


16 


30 




14 


50 


46 


128 


#c 


29 


18 




80 


41 


-41 


29 


14 




86 


61 


21 


#o 


01 


05 


80 




31 


—24 


19 


50 


86 




79 


57 


#E 


34 


25 


41 


31 




49 


39 


46 


61 


79 




92 


#F 


—11 


16 


—41 


—24 


49 




10 


128 


21 


57 


92 





SECTION VII 
BIBLIOGRAPHY 

Bonser, Frederick G. (1910) The Reasoning Ability of School Children 
of the Fourth, Fifth, and Sixth School Grades. (Contributions to 
Education, No. 37.) Teachers College, Columbia University. 

Briggs, Thomas Henry (1913) Formal English Grammar as a Discipline. 
Teachers College Record, September, 1913. 

Burt, Cyril and Moore, Robert C (1912) The Mental Differences be- 
tween the Sexes. Journal of Experimental Pedagogy, 1912, pages 
273 to 284 and 355 to 388. 

de Fursac, J. Rogues (1913) Manual of Psychiatry. John Wiley and 
Sons. 

Goddard, Henry H. (1911) The Binet-Simon Measuring Scale for In- 
telligence. Revised Edition. 

Hart, Bernard and Spearman C. (1912) General Ability, Its Existence 
and Nature. British Journal of Psychology, Vol. V. 

Spearman, C. (1904) General Intelligence objectively determined and 
measured. American Journal of Psychology, Vol. XV, No. 2. 
(1914) The Theory of Two Factors. Psychological Review. 

Starch, Daniel (1915) The Measurement of Achievement in English 
Grammar. Journal of Educational Psychology, December, 1915, p. 
615ff. 

(1916) A Scale for Measuring Ability in Arithmetic. Journal of 
Educational Psychology, April, 1916, pp. 213ff. 

Thompson, Helen B. (Mrs. Woolley) (1903) Psychological Norms in 
Men and Women. University of Chicago Contributions to Phil- 
osophy, Vol. 4, No. 1. 

Thorndike, Edward Lee (1914) Educational Psychology, 3 vols. Teach- 
ers College, Columbia University. 

(1914) The Measurement of Ability in Reading. Teachers College 
Record, September, 1914. 

Woodworth, R. S. and Wells, F. L. (1911) Association Tests. Psycho- 
logical Review Monographs, Vol. 13, 1911, No. 57. 

Woody, Clifford (1916) Measurements of Some Achievements in Arith- 
metic. (Contributions to Education, No. 80.) Teachers College, 
Columbia University. 



ACKNOWLEDGMENTS 

The thanks of the writer are due to: 

Mr. J. H. Smallen, principal of the school in which the tests 
were given; the Misses E. M. Hammer and A. S. Sainsbury, 
the teachers of the two classes, and several other teachers, all 
of whom showed kindness and a spirit of cooperation toward 
the writer. 

The members of the New York State Commission on Ventila- 
tion : Messrs. C.-E. A. Winslow, D. D. Kimball, F. S. Lee, J. A. 
Miller, E. B. Phelps, and E. L. Thorndike, who were kind enough 
to permit the writer to use some of the records which had been 
obtained for them from the same pupils. The tests, which were 
given, scored, and tabulated under the direction of this committee, 
are C3, C4, C5, C6, C7, C8, D5, D6, E7, E8, Eo, Eio, E13, E14, 
E15, E16, and E18. 

Miss Agnes Low Rogers, of Goucher College, who presented, 
scored, and tabulated four tests: Bi, B2, B3, and B4. 

Dr. Marvin James Van Wagenen, of the University of Minne- 
sota, who presented, scored, and tabulated two tests : E5 and E6. 

The members of the thesis committee : Dr. H. A. Ruger, 
assistant professor of educational psychology, Teachers College, 
who designed the Puzzles tests ; the late Dr. Naomi Norsworthy. 
associate professor of educational psychology, Teachers College ; 
Dr. Robert Sessions Wood worth, professor of psychology, Co- 
lumbia University, and for general assistance and advice, espe- 
cially Dr. Edward Lee Thorndike, professor of educational 
psychology, Teachers College. 



